This application is the National Stage of International Application No. PCT/JP99/05786, filed on Oct. 20, 1999.
The present invention relates to condensed pyridazine derivatives exhibiting an excellent anti-allergic, anti-histaminic, anti-inflammatory or eosinophil chemotaxis-inhibiting activity, or other activities, and useful as an agent for treating or preventing atopic dermatitis, allergic rhinitis, bronchial asthma, allergic conjunctivitis, chronic urticaria, etc., their pro-drugs, methods for producing them and use.
Many condensed pyridazine derivatives are currently synthesized as drugs for a variety of diseases. For example, U.S. Pat. No. 3,915,968 discloses a compound represented by the formula: 
wherein R and R3 independently represent a hydrogen atom or a lower alkyl group (at least one of R and R3 is a lower alkyl group); R1 and R2 represent a heterocyclic group selected from the group consisting of pyrrolidine, piperidine, piperazine and morpholine taken together with the adjacent nitrogen atom; or a salt thereof. U.S. Pat. No. 4,136,182 is closes that a compound represented by the formula: 
wherein R represents a hydrogen atom, a phenyl group or a lower alkylcarbonylamino group; R1 represents morpholino or piperidino; R2represents a hydrogen atom or a lower alkyl group (at least one of R and R2is a group other than a hydrogen atom; when R is a phenyl group, R1 is morpholino and R2 is a lower alkyl group); or a salt thereof, is useful as a bronchodilator for mitigating bronchial spasms.
Also, Japanese Patent Unexamined Publication No. 279447/1995 discloses that a compound represented by the formula: 
wherein R1 represents a hydrogen atom, a lower alkyl group that may be substituted, or a halogen atom; R2 and R3 independently represent a hydrogen atom or a lower alkyl group which may be substituted, or may form a 5- to 7-membered ring with the adjacent xe2x80x94Cxe2x95x90Cxe2x80x94; X represents an oxygen atom or S(O)p (p represents an integer of 0 to 2); Y represents a group represented by the formula: 
(R4 and R5 independently represent a hydrogen atom or a lower alkyl group which may be substituted) or a divalent group derived from a 3- to 7-membered homocycle or heterocycle which may be substituted; R6 and R7 independently represent a hydrogen atom, a lower alkyl group which may be substituted, a cycloalkyl group which may be substituted, or an aryl group that may be substituted, or may form a nitrogen-containing heterocyclic group which may be substituted, with the adjacent nitrogen atom; m represents an integer from 0 to 4, and n represents an integer from 0 to 4; or a salt thereof; and, as an example synthetic product, a compound of the formula: 
exhibits anti-asthmatic, anti-PAF, anti-inflammatory and anti-allergic activities.
Furthermore, Japanese Patent Unexamined Publication No. 279446/1995 describes a compound represented by the formula: 
wherein R1 represents a hydrogen atom, a lower alkyl group which may be substituted, or a halogen atom; R2 and R3 independently represent a hydrogen atom or a lower alkyl group which may be substituted (provided that either of R2 and R3 is a hydrogen atom, the other represents a lower alkyl group which may be substituted), or may form a 5- to 7-membered ring taken together with the adjacent xe2x80x94Cxe2x95x90Cxe2x80x94; X represents an oxygen atom or S(O)p (p represents an integer of 0 to 2): Y represents a group represented by the formula: 
(R4 and R5 independently represent a hydrogen atom or a lower alkyl group which may be substituted) or a divalent group derived from a 3- to 7-membered homocycle or heterocycle which may be substituted; R6 and R7 independently represent a hydrogen atom, a lower alkyl group which may be substituted, a cycloalkyl group which may be substituted, or an aryl group which may be substituted, or may form a nitrogen-containing heterocyclic group which may be substituted, taken together with the adjacent nitrogen atom; m represents an integer from 0 to 4, and n represents an integer from 0 to 4; or a salt thereof; and discloses that these compounds possess anti-allergic, anti-inflammatory and anti-PAF (platelet activating factor) activities to suppress bronchial spasms and bronchial contraction, therefore could be utilized as effective anti-asthmatic agents.
On the other hand, as compounds exhibiting anti-allergic or anti-histaminic activities, there may be mentioned, for example, terfenadine (The Merck Index, 12th edition, 9307) and ebastine (The Merck Index, 12th edition, 3534), which are already in clinical use.
And, EP128536 discloses anti-bacterial compounds represented by the formula: 
and so on, and U.S. Pat. No. 4,499,088 discloses anti-bacterial compounds represented by the formula: 
and so on. However, they never disclose about anti-allergic action, anti-histaminic action, anti-inflammatory action and so on.
There is demand for the development of novel compounds more satisfactory than conventional anti-allergic agents, anti-histaminic agents, anti-inflammatory agents in terms of action efficacy, sustained action, safety etc., their production and novel pharmaceutical composition.
Through various extensive investigations, the present inventors found that condensed pyridazine compounds represented by the formula: 
wherein Ar1 and Ar2 are independently an aromatic group which may be substituted, and Ar1 and Ar2 may form a condensed cyclic group with an adjacent carbon atom; ring B is a nitrogen-containing heterocycle may be substituted; X and Y are the same or different and are independently a bond, an oxygen atom, S(O)p (p is an integer of 0 to 2), NR4 wherein R4 is a hydrogen atom or a lower alkyl group, or a divalent linear lower hydrocarbon group which may contain 1 to 3 hetero atoms and the bivalent linear lower hydrocarbon group may be substituted; A is a nitrogen atom or CR7 (R7 is a hydrogen atom, a halogen atom, a hydrocarbon group optionally having a substituent, an acyl group or a hydroxy group optionally having a substituent; R1, R2and R3are the same or different and are independently a hydrogen atom, a halogen atom, a hydrocarbon group optionally having a substituent, an acyl group or a hydroxy group which may be substituted; R8 is a hydrogen atom, a hydroxy group which may be substituted by lower alkyl or a carboxyl group; provided that the nitrogen-containing heterocycle represented by ring B is not a heterocycle represented by the formula: 
wherein n is 0 or 1, or a salt thereof, owing to their unique chemical structure characterized by the presence of substitutional piperidine or piperazine via a spacer from the 6-position of the [1,2,4]triazolo[1,5-b]pyridazine or imidazo[1,2-b]pyridazine skeleton, exhibits unexpectedly excellent activities for preventing or treating allergic skin diseases such as contact dermatitis, pruritus and so on.
And, the present inventors found that condensed pyridazine derivatives represented by the formula: 
wherein Ar1xe2x80x2 and Ar2xe2x80x2 are independently an aromatic group optionally having a substituent, and Ar1xe2x80x2 and Ar2xe2x80x2 may form a condensed cyclic group with an adjacent carbon atom; ring Bxe2x80x2 is a nitrogen-containing heterocycle optionally having a substituent; X and Y are the same or different and are independently a bond, an oxygen atom, S(O)p (p is an integer of 0 to 2), NR4 wherein R4 is a hydrogen atom or a lower alkyl group, or a bivalent linear lower hydrocarbon group which may contain 1 to 3 hetero atoms and the bivalent linear lower hydrocarbon group may be substituted; A is a nitrogen atom or CR7 wherein R7 is a hydrogen atom, a halogen atom, a hydrocarbon optionally having a substituent, an acyl group or a hydroxy group optionally having a substituent; R1 is a hydrocarbon group substituted with an optionally esterified carboxyl group, R2and R3 are the same or different and are independently a hydrogen atom, a halogen atom, a hydrocarbon group optionally having a substituent, an acyl group or a hydroxy group optionally having a substituent; R8 is a hydrogen atom, a hydroxy group which may be substituted by lower alkyl or a carboxyl group, or a salt thereof, owing to their unique chemical structure characterized by the presence of substitutional piperidine or piperazine via a spacer from the 6-position of the [1,2,4]triazolo[1,5-b]pyridazine or imidazo[1,2-b]pyridazine skeleton, can be produced in good efficiency and in a high yield.
Furthermore, the inventors found that among the above mentioned compound (I) or a salt thereof, a hydrate of a compound represented by the formula: 
wherein R is a hydrogen atom or an ethyl group, or a succinate or citrate of the compound (Ixe2x80x3) and 2-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]-3-methylimidazo[1,2-b]pyridazin-2-yl]-2-methylpropionic acid or a salt thereof, which are excellent in stability, exhibit an excellent anti-allergic activity.
The inventors conducted further investigations based on these findings, and developed the present invention.
The present invention provides:
1. A pharmaceutical composition for preventing or treating allergic skin diseases which comprises a compound represented by the formula: 
wherein Ar1 and Ar2 are independently an aromatic group optionally having a substituent, and Ar1 and Ar2 may form a condensed cyclic group with an adjacent carbon atom; ring B is a nitrogen-containing heterocycle optionally having a substituent; X and Y are the same or different and are independently a bond, an oxygen atom, S(O)p (p is an integer of 0 to 2), NR4 wherein R4 is a hydrogen atom or a lower alkyl group, or a bivalent linear lower hydrocarbon group which may contain 1 to 3 hetero atoms and the bivalent linear lower hydrocarbon group may be substituted; A is a nitrogen atom or CR7 wherein R7 is a hydrogen atom, a halogen atom, a hydrocarbon optionally having a substituent, an acyl group or a hydroxy group optionally having a substituent; R1, R2 and R3 are the same or different and are independently a hydrogen atom, a halogen atom, a hydrocarbon group optionally having a substituent, an acyl group or a hydroxy group optionally having a substituent; R8 is a hydrogen atom, a hydroxy group which may be substituted by a lower alkyl group or a carboxyl group, provided that the nitrogen-containing heterocycle represented by ring B is not a heterocycle represented by the formula: 
wherein n is 0 or 1, or a salt thereof, or a pro-drug thereof,
2. A pharmaceutical composition as defined in term 1 wherein the allergic skin disease is contact dermatitis, pritus, dried dermatitis, acute urticaria or prurigo,
3. A pharmaceutical composition as defined in term 1 wherein Ar1 and Ar1 are independently (1) a C6-14 aromatic hydrocarbon group, (2) a 5 to 8 membered aromatic heterocyclic group containing 1 to 4 hetero atoms selected from a nitrogen atom, a sulfur atom and an oxygen atom other than carbon atoms or (3) a group removed a hydrogen atom from a condensed ring formed by the 5 to 8 membered aromatic heterocyclic group and the C6-14 aromatic hydrocarbon group, and the C6-14 aromatic hydrocarbon group, the 5 to 8 membered aromatic heterocyclic group and the group formed by the 5 to 8 membered aromatic heterocyclic group and the C6-14 aromatic hydrocarbon group may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkyl sulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy and (xxviii) C7-16 aralkyloxy; and A1 and Ar2 may form a condensed cyclic group with the adjacent carbon atom represented by the formula: 
wherein R8 is a hydrogen atom, a hydroxy group which may be substituted by C1-6 alkyl or a carboxyl group, and the condensed cyclic group may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxix) oxo;
the ring B is a 3 to 13 membered nitrogen-containing heterocycle containing at least one nitrogen atom which may contain 1 to 3 hetero atoms selected from a nitrogen atom, an oxygen atom and a sulfur atom, and the 3 to 13 membered nitrogen-containing heterocycle may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi)mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxix) oxo;
X and Y are same or different {circle around (1)} a bond, {circle around (2)} an oxygen atom, {circle around (3)} S(O)p wherein p is an integer of 0 to 2, {circle around (4)} NR4 wherein R4 is a hydrogen atom or a linear or branched C1-6 alkyl group or {circle around (5)} a bivalent linear C1-6 hydrocarbon group which may contain 1 to 3 hetero atoms selected from an oxygen atom and a sulfur atom, and the bivalent linear C1-6 hydrocarbon group may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxix) oxo;
A is a nitrogen atom or CR7 wherein R7 is
(1) a hydrogen atom,
(2) a halogen atom,
(3) a C1-6 alkyl group, a C2-6 alkenyl group, a C2-6 alkynyl group, a C3-6 cycloalkyl group condensed group formed by a C3-6 cycloalkyl group and a benzene ring optionally having 1 to 3 substituents selected from the group consisting of C1-6 alkoxy, a C6-14 aryl group and a C7-16 aralkyl group, which may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxycarbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy
(4) an acyl group represented by the formula: xe2x80x94(Cxe2x95x90O)xe2x80x94R9, xe2x80x94SO2xe2x80x94R9, xe2x80x94SOxe2x80x94R9, xe2x80x94(Cxe2x95x90O)NR10R9, xe2x80x94(Cxe2x95x90O)Oxe2x80x94R9, xe2x80x94(Cxe2x95x90S)Oxe2x80x94R9 or xe2x80x94(Cxe2x95x90S)NR10R9 wherein R9 is (a) a hydrogen atom, (b) a C1-6 alkyl group, a C2-6 alkenyl group, a C2-6 alkynyl group, a C3-6 cycloalkyl group, a condensed group formed by a C3-6 cycloalkyl group and a benzene ring optionally having 1 to 3 substituents selected from the group consisting of C1-6 alkoxy, a C6-14 aryl group and a C7-16 aralkyl group, which may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxix) oxo or (c) a group represented by the formula: xe2x80x94OR11 wherein R11 is a hydrogen atom or a C1-6 alkyl group, a C2-6 alkenyl group, a C2-6 alkynyl group, a C3-6 cycloalkyl group, a condensed group formed by a C3-6 cycloalkyl group and a benzene ring optionally having 1 to 3 substituents selected from the group consisting of C1-6 alkoxy, a C6-14 aryl group and a C716 aralkyl group, which may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkylcarbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxix) oxo, R10 is a hydrogen atom or a C1-6 alkyl group, or
(5) a group represented by the formula: xe2x80x94OR12 wherein R12 is a hydrogen atom, or a C1-6 alkyl group, a C2-6 alkenyl group, a C2-6 alkynyl group, a C3-6 cycloalkyl group, a condensed group formed by a C3-6 cycloalkyl group and a benzene ring optionally having 1 to 3 substituents selected from the group consisting of C1-6 alkoxy, a C6-14 aryl group and a C7-16 aralkyl group, which may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxix) oxo
R1, R2 and R3 are the same or different and are independently
(1) a hydrogen atom,
(2) a halogen atom,
(3) a C1-6 alkyl group, a C2-6 alkenyl group, a C2-6 alkynyl group, a C3-6 cycloalkyl group condensed group formed by a C3-6 cycloalkyl group and a benzene ring optionally having 1 to 3 substituents selected from the group consisting of C1-6 alkoxy, a C6-14 aryl group and a C7-16 aralkyl group, which may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv); 5 or 6 membered cyclic amino, (xvi) C1-6 alkylcarbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxviii) oxo,
(4) an acyl group represented by the formula: xe2x80x94(Cxe2x95x90O)xe2x80x94R13, xe2x80x94SO2xe2x80x94R13, xe2x80x94SOxe2x80x94R13, xe2x80x94(Cxe2x95x90O)NR14R13, xe2x80x94(Cxe2x95x90O)Oxe2x80x94R13, xe2x80x94(Cxe2x95x90S)Oxe2x80x94R13 or xe2x80x94(Cxe2x95x90S)NR14R13 wherein R13 is (a) a hydrogen atom, (b) a C1-6 alkyl group, a C2-6 alkenyl group, a C2-6 alkynyl group, a C3-6 cycloalkyl group, a condensed group formed by a C3-6 cycloalkyl group and a benzene ring optionally having 1 to 3 substituents selected from the group consisting of C1-6 alkoxy, a C6-14 aryl group and a C7-16 aralkyl group, which may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxix) oxo or (c) a group represented by the formula: xe2x80x94OR15 wherein R15 is a hydrogen atom, or a C1-6 alkyl group, a C2-6 alkenyl group, a C2-6 alkynyl group, a C3-6 cycloalkyl group, a condensed group formed by a C3-6 cycloalkyl group and a benzene ring optionally having 1 to 3 substituents selected from the group consisting of C1-6 alkoxy, a C6-14 aryl group and a C7-16 aralkyl group, which may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkylcarbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxix) oxo;
R14 is a hydrogen atom or a C1-6 alkyl group; or
(5) a group represented by the formula: xe2x80x94OR16 wherein R16 is a hydrogen atom, or a C1-6 alkyl group, a C2-6 alkenyl group, a C2-6 alkynyl group, a C3-6 cycloalkyl group, a condensed group formed by a C3-6 cycloalkyl group and a benzene ring optionally having 1 to 3 substituents selected from the group consisting of C1-6 alkoxy, a C6-14 aryl group and a C7-16 aralkyl group, which may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxix) oxo:
R8 is a hydrogen atom, a hydroxy group which may be substituted by C1-6 alkyl or a carboxyl group,
4. A pharmaceutical composition as defined in term 1 wherein Ar1 and Ar2 are independently (1) a phenyl group which may be substituted by a halogen atom or C1-6 alkyl or (2) a 5 to 8 membered aromatic heterocyclic group containing 1 to 4 hetero atoms selected from a nitrogen atom, a sulfur atom and an oxygen atom other than carbon atoms; the ring B is a ring represented by the formula: 
wherein Z is a nitrogen atom or a methyne group; Z1 and Z2 is independently a linear C1-4 alkylene group which may be substituted by a hydroxy group, an oxo group or a C1-6 alkyl group; X is a bond, an oxygen atom or NH; Y is
(i) a C1-6 alkylene group,
(ii) xe2x80x94(CH2)p1Oxe2x80x94,
(iii) xe2x80x94(CH2)xe2x80x94p1NHxe2x80x94,
(iv) xe2x80x94(CH2)p1Sxe2x80x94,
(v) xe2x80x94(CH2)q1CH(OH)(CH2)q2Oxe2x80x94,
(vi) xe2x80x94(CH2)q1CH(OH)(CH2)q2NHxe2x80x94,
(vii) xe2x80x94(CH2)q1CH(OH)(CH2)q2Sxe2x80x94,
(viii) xe2x80x94(CH2)p1CONHxe2x80x94,
(ix) xe2x80x94COO(CH2)p1Oxe2x80x94,
(x) xe2x80x94COO(CH2)p1NHxe2x80x94,
(xi) xe2x80x94COO(CH2)p1Sxe2x80x94,
(xii) xe2x80x94(CH2)q1O(CH2)q2Oxe2x80x94,
(xiii) xe2x80x94(CH2)q1O(CH2)q2NHxe2x80x94 or
(xiv) xe2x80x94(CH2)q1O(CH2)q2Sxe2x80x94 wherein p1 is an integer of 1 to 6, q1 and q2 are an integer of 1 to 3; A is a nitrogen atom or CR7xe2x80x2 wherein R7xe2x80x2 is a hydrogen atom, a halogen atom, a C1-6 alkyl group, a C1-6 alkoxy-carbonyl group or a carboxyl group; R1 is (1) a hydrogen atom, (2) a C1-6 alkyl group which maybe substituted by carboxyl, C1-6 alkoxy-carbonyl, hydroxy or carbamoyl optionally having mono- or di-C1-6 alkyl, (3) a C6-14 aryl group, (4) a C1-6 alkoxy group, (5) a C1-6 alkoxy-carbonyl group, (6) a carboxyl group, (7) a carbamoyl group which may be substituted by a C1-6 alkyl group optionally having carboxyl or C1-6 alkoxy-carbonyl or (8) a C3-6 cycloalkyl group which may be substituted by C1-6 alkoxy-carbonyl; R2 is a hydrogen atom, a C1-6 alkyl group, a C1-6 alkoxy-carbonyl group or a carboxyl group; R3 is a hydrogen atom; R8 is a hydrogen atom or a hydroxyl group,
5. A pharmaceutical composition as defined in term 1 wherein Ar1 and Ar2 are a phenyl group; the ring B is a ring represented by the formula: 
wherein Zxe2x80x2 is a methyne group; Z1xe2x80x2 and Z2xe2x80x2 are a methylene group or an ethylene group; X is a bond or an oxygen atom; Y is xe2x80x94(CH2)p1NHxe2x80x94 wherein p1 is an integer of 1 to 6; A is CR7xe2x80x3 wherein R7xe2x80x3 is a hydrogen atom or a C1-6 alkyl group; R1 is (1) a hydrogen atom, (2) a C1-6 alkyl group which may be substituted by carboxyl or C1-6 alkoxy-carbonyl or (3) a carbamoyl group which may be substituted by a C1-6 alkyl group optionally having C1-6 alkoxy-carbonyl; R2 is a hydrogen atom; R3 is a hydrogen atom; R8 is a hydrogen atom,
6. A pharmaceutical composition as defined in term 1 wherein the compound is
2-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]imidazo[1,2-b]pyridazin-2-yl]-2-methylpropionic acid or a salt thereof,
7. A pharmaceutical composition as defined in term 1 wherein the compound is
2-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]imidazo[1,2-b]pyridazin-2-yl]-2-methylpropionic acid dihydrate,
8. A method for preventing or treating allergic skin diseases which comprises administering an effective amount of a compound represented by the formula: 
wherein Ar1 and Ar2 are independently an aromatic group optionally having a substituent, and Ar1 and Ar2 may form a condensed cyclic group with an adjacent carbon atom; ring B is a nitrogen-containing heterocycle optionally having a substituent; X and Y are the same or different and are independently a bond, an oxygen atom, S(O)p (p is an integer of 0 to 2), NR4 wherein R4 is a hydrogen atom or a lower alkyl group, or a bivalent linear lower hydrocarbon group which may contain 1 to 3 hetero atoms and the bivalent linear lower hydrocarbon group may be substituted; A is a nitrogen atom or CR7 wherein R7 is a hydrogen atom, a halogen atom, a hydrocarbon optionally having a substituent, an acyl group or a hydroxy group optionally having a substituent; R1, R2 and R3 are the same or different and are independently a hydrogen atom, a halogen atom, a hydrocarbon group optionally having a substituent, an acyl group or a hydroxy group optionally having a substituent; R8 is a hydrogen atom, a hydroxy group which may be substituted by lower alkyl or a carboxyl group, provided that the nitrogen-containing heterocycle represented by ring B is not a heterocycle represented by the formula: 
wherein n is 0 or 1, or a salt thereof, or a pro-drug thereof to mammals,
9. A method for preventing to treating as defined in term 8 wherein the allergic skin disease is contact dermatitis, pruritus, dried dermatitis, acute urticaria or prurigo,
10. Use of a compound represented by the formula: 
wherein Ar1 and,Ar2 are independently an aromatic group optionally having a substituent, and Ar1 and Ar2 may form a condensed cyclic group with an adjacent carbon atom; ring B is a nitrogen-containing heterocycle optionally having a substituent; X and Y are the same or different and are independently a bond, an oxygen atom, S(O)p (p is an integer of 0 to 2), NR4 wherein R4 is a hydrogen atom or a lower alkyl group, or a bivalent linear lower hydrocarbon group which may contain 1 to 3 hetero atoms and the bivalent linear lower hydrocarbon group may be substituted; A is a nitrogen atom or CR1 wherein R7 is a hydrogen atom, a halogen atom, a hydrocarbon optionally having a substituent, an acyl group or a hydroxy group optionally having a substituent; R1, R2 and R3 are the same or different and are independently a hydrogen atom, a halogen atom, a hydrocarbon group optionally having a substituent, an acyl group or a hydroxy group optionally having a substituent; R8 is a hydrogen atom, a hydroxy group which may be substituted by a lower alkyl group or a carboxyl group, provided that the nitrogen-containing heterocycle represented by ring B is not a heterocycle represented by the formula: 
wherein n is 0 or 1, or a salt thereof, or a pro-drug thereof for preparing a pharmaceutical composition for preventing or treating allergic skin diseases,
11. Use as defined in term 10 wherein the allergic skin disease is contact dermatitis, pruritus, dried dermatitis, acute urticaria or prurigo,
12. A method for producing a compound represented by the formula: 
wherein Ar1xe2x80x2 and Ar2xe2x80x2 are independently an aromatic group optionally having a substituent, and Ar1xe2x80x2 and Ar2xe2x80x2 may form a condensed cyclic group with an adjacent carbon atom; ring Bxe2x80x2 is a nitrogen-containing heterocycle optionally having a substituent; X and Y are the same or different and are independently a bond, an oxygen atom, S(O)p (p is an integer of 0 to 2), NR4 wherein R4 is a hydrogen atom or a lower alkyl group, or a bivalent linear lower hydrocarbon group which may contain 1 to 3 hetero atoms and the bivalent linear lower hydrocarbon group may be substituted; A is a nitrogen atom or CR7 wherein R7 is a hydrogen atom, a halogen atom, a hydrocarbon optionally having a substituent, an acyl group or a hydroxy group optionally having a substituent; R1xe2x80x2 is a hydrocarbon group substituted by an optionally esterified carboxyl group; R2 and R3 are the same or different and are independently a hydrogen atom, a halogen atom, a hydrocarbon group optionally having a substituent, an acyl group or a hydroxy group optionally having a substituent; R8 is a hydrogen atom, a hydroxy group which may be substituted by a lower alkyl group or a carboxyl group, or a salt thereof, which comprises reacting a compound represented by the formula: 
wherein Q1 represents a leaving group; the other symbols are same as defined in the above, or a salt thereof, with a compound represented by the formula: 
wherein Q2 represents a leaving group; the other symbols are same as defined above, or a salt thereof in a solvent or/and in the presence of a base, and if necessary in an atmosphere of inert gas,
13. A method as defined in term 12 wherein the solvent is a non-protic solvent having a high boiling point,
14. A method as defined in term 12 wherein the solvent is sulfoxides,
15. A method as defined in term 12 wherein the solvent is a dimethyl sulfoxide,
16. A method as defined in term 12 wherein the base is an alkali metal carbonate,
17. A method as defined in term 12 wherein the base is a sodium carbonate,
18. A method as defined in term 12 wherein the reaction is conducted in the solvent and in the presence of a base,
19. A method as defined in term 12 wherein the reaction is further conducted in the presence of halogenated alkali metals,
20. A method as defined in term 19 wherein halogenated alkali metal is a sodium bromide,
21. A method as defined in term 12 wherein Ar1xe2x80x2 and Ar2xe2x80x2 are a C6-14 single cyclic or condensed cyclic aromatic hydrocarbon group which may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy and (xxviii) C7-16 aralkyloxy; and Ar1xe2x80x2, Ar2xe2x80x2 and the adjacent carbon atom may form a condensed cyclic group represented by the formula: 
wherein R8 is a hydrogen atom, a hydroxy group which may be substituted by C1-6 alkyl or a carboxyl group, and the condensed cyclic group may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxix) oxo;
the ring Bxe2x80x2 is a 6-membered: nitrogen-containing heterocycle which may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxix) oxo;
X and Y are same or different and are independently {circle around (1)} a bond, {circle around (2)} an oxygen atom, {circle around (3)} S(O)p wherein p is an integer of 0 to 2, {circle around (4)} NR4 wherein R4 is a hydrogen atom or a linear or branched C1-6 alkyl group or {circle around (5)} a bivalent linear C1-6 hydrocarbon group which may contain 1 to 3 hetero atoms selected from an oxygen atom and a sulfur atom, and the bivalent linear C1-6 hydrocarbon group may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-4 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxix) oxo;
A is a nitrogen atom or CR7 wherein R7 is
(1) a hydrogen atom,
(2) a halogen atom,
(3) a C1-6 alkyl group, a C2-6 alkenyl group, a C2-6 alkynyl group, a C3-6 cycloalkyl group, a condensed group formed by a C3-6 cycloalkyl group and a benzene ring optionally having 1 to 3 substituents selected from the group consisting of C1-6 alkoxy, a C6-14 aryl group and a C7-16 aralkyl group, which may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkylcarbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxix) oxo,
(4) an acyl group represented by the formula: xe2x80x94(Cxe2x95x90O)xe2x80x94R9, xe2x80x94SO2xe2x80x94R9, xe2x80x94SOxe2x80x94R9, xe2x80x94(Cxe2x95x90O)NR10R9, xe2x80x94(Cxe2x95x90O)Oxe2x80x94R9, xe2x80x94(Cxe2x95x90S)Oxe2x80x94R9 or xe2x80x94(Cxe2x95x90S)NR10R9 wherein R9 is (a) a hydrogen atom, (b) a C1-6 alkyl group, a C2-6 alkenyl group, a C2-6 alkynyl group, a C3-6 cycloalkyl group, a condensed group formed by a C3-6 cycloalkyl group and a benzene ring optionally having 1 to 3 substituents selected from the group consisting of C1-6 alkoxy, a C6-14 aryl group and a C7-16 aralkyl group, which may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxix) oxo or (c) a group represented by the formula: xe2x80x94OR11 wherein R11 is a hydrogen atom, or a C1-6 alkyl group, a C2-6 alkenyl group, a C2-6 alkynyl group, a C3-6 cycloalkyl group, a condensed group formed by a C3-6 cycloalkyl group and a benzene ring optionally having 1 to 3 substituents selected from the group consisting of C1-6 alkoxy, a C6-14 aryl group and a C7-16 aralkyl group, which may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxix) oxo,
R10 is a hydrogen atom or a C1-6 alkyl group, or
(5) a group represented by the formula: xe2x80x94OR12 wherein R12 is a hydrogen atom, or a C1-6 alkyl group, a C2-6 alkenyl group, a C2-6 alkynyl group, a C3-6 cycloalkyl group, a condensed group formed by a C3-6 cycloalkyl group and a benzene ring optionally having 1 to 3 substituents selected from the group consisting of C1-6 alkoxy, a C6-14 aryl group and a C7-16 aralkyl group, which may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxix) oxo;
R1xe2x80x2 is a C1-6 alkyl group, a C2-6 alkenyl group, a C2-6 alkynyl group, a C3-6 cycloalkyl group, condensed group formed by a C3-6 cycloalkyl group and a benzene ring optionally having 1 to 3 substituents selected from the group consisting of C1-6 alkoxy, a C6-14 aryl group and a C7-16 aralkyl group which is substituted by a group represented by the formula: xe2x80x94COOR11 wherein R11 is (1) a hydrogen atom or (2) a C1-6 alkyl group, a C2-6 alkenyl group, a C2-6 alkynyl group, a C3-6 cycloalkyl group, a condensed group formed by a C3-6 cycloalkyl group and a benzene ring optionally having 1 to 3 substituents selected from the group consisting of C1-6 alkoxy, a C6-14 aryl group e and a C7-16 aralkyl group which may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino (v) and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkyl sulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7 -16 aralkyloxy and (xxix) oxo;
R2 and R3 are the same or different and are independently
(1) a hydrogen atom,
(2) a halogen atom,
(3) a C1-6 alkyl group, a C2-6 alkenyl group, a C2-6 alkynyl group, a C3-6 cycloalkyl group, a condensed group formed by a C3-6 cycloalkyl group and a benzene ring optionally having 1 to 3 substituents selected from the group consisting of C1-6 alkoxy, a C6-14 aryl group and a C7-16 aralkyl group, which may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxix) oxo,
(4) an acyl group represented by the formula: xe2x80x94(Cxe2x95x90O)xe2x80x94R13, xe2x80x94SO2xe2x80x94R13, xe2x80x94SOxe2x80x94R13, xe2x80x94(Cxe2x95x90O)NR14R13, xe2x80x94(Cxe2x95x90O)Oxe2x80x94R13, xe2x80x94(Cxe2x95x90S)Oxe2x80x94R13 or xe2x80x94(Cxe2x95x90S)NR14R13 wherein R13 is (a) a hydrogen atom, (b) a C1-6 alkyl group, a C2-6 alkenyl group, a C2-6 alkynyl group, a C3-6 cycloalkyl group, a condensed group formed by a C3-6 cycloalkyl group and a benzene ring optionally having 1 to 3 substituents selected from the group consisting of C1-6 alkoxy, a C6-14 aryl group and a C7-16 aralkyl group, which may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy; (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxix) or (c) a group represented by the formula: xe2x80x94OR15 wherein R15 is a hydrogen atom, or a C1-6 alkyl group, a C2-6 alkenyl group, a C2-6 alkynyl group, a C3-6 cycloalkyl group, a condensed group formed by a C3-6 cycloalkyl group and a benzene ring optionally having 1 to 3 substituents selected from the group consisting of C1-6 alkoxy, a C6-14 aryl group and a C7-16 aralkyl group, which may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxix) oxo,
R14 is a hydrogen atom or a C1-6 alkyl group; or
(4) a group represented by the formula: xe2x80x94OR16 wherein R16 is a hydrogen atom, or a C1-6 alkyl group, a C2-6 alkenyl group, a C2-6 alkynyl group, a C3-6 cycloalkyl group, a condensed group formed by a C3-6 cycloalkyl group and a benzene ring optionally having 1 to 3 substituents selected from the group consisting of C1-6 alkoxy, a C6-14 aryl group and a C7-16 aralkyl group, which may be substituted by a group selected from the group consisting of (i) a halogen atom, (ii) C1-6 alkylenedioxy, (iii) nitro, (iv) cyano, (v) optionally halogenated C1-6 alkyl, (vi) optionally halogenated C2-6 alkenyl, (vii) optionally halogenated C2-6 alkynyl, (viii) C3-6 cycloalkyl, (ix) C1-6 alkoxy optionally having 1 to 3 substituents selected from the group consisting of halogen atoms, mono- or di-C1-6 alkylamino and C1-6 alkoxy-carbonyl, (x) optionally halogenated C1-6 alkylthio, (xi) hydroxy, (xii) amino, (xiii) mono-C1-6 alkylamino, (xiv) di-C1-6 alkylamino, (xv) 5 or 6 membered cyclic amino, (xvi) C1-6 alkyl-carbonyl, (xvii) carboxyl, (xviii) C1-6 alkoxy-carbonyl, (xix) carbamoyl, (xx) thiocarbamoyl, (xxi) mono-C1-6 alkyl-carbamoyl, (xxii) di-C1-6 alkyl-carbamoyl, (xxiii) C6-10 aryl-carbamoyl, (xxiv) sulfo, (xxv) C1-6 alkylsulfonyl, (xxvi) C6-10 aryl, (xxvii) C6-10 aryloxy, (xxviii) C7-16 aralkyloxy and (xxix) oxo;
R8 is a hydrogen atom, a hydroxy group which may be substituted by a C1-6 alkyl group or a carboxyl group,
22. A method for producing a compound as defined in term 12 wherein
(1) Ar1xe2x80x2 and Ar2xe2x80x2 are independently a phenyl group; ring Bxe2x80x2 is 
X is an oxygen atom; Y is a propylamino group; R8 is a hydrogen atom; A is CH; R1xe2x80x2 is a carboxyl dimethylmethyl group; and R2 and R3 are a hydrogen atom,
(2) Ar1xe2x80x2 and Ar2xe2x80x2 are independently a phenyl group; ring Bxe2x80x2 is 
X is an oxygen atom; Y is a propylamino group; R8 is a hydrogen atom; A is CH; R1xe2x80x2 is an ethoxycarbonyl dimethylmethyl group; and R2 and R3 are a hydrogen atom,
(3) Ar1xe2x80x2 and Ar2xe2x80x2 are independently a phenyl group; ring Bxe2x80x2 is 
X is an oxygen atom; Y is a propylamino group; R8 is a hydrogen atom; A is CH; R1xe2x80x2 is a carboxyl dimethylmethyl group; R2 and R3 are a hydrogen atom; the solvent is a dimethylsulfoxide and the base is a sodium carbonate, or
(4) Ar1xe2x80x2 and Ar2xe2x80x2 are independently a phenyl group; ring Bxe2x80x2 is 
X is an oxygen atom; Y is a propylamino group; R8 is a hydrogen atom; A is CH; R1xe2x80x2 is an ethoxycarbonyl dimethylmethyl group; R2 and R3 are a hydrogen atom; the solvent is a 1-methyl-2-pyrrolidone and the base is a sodium carbonate,
23. A method for producing a compound as defined in term 12 wherein the leaving group represented by Q1 is a hydrogen atom or an alkali metal,
24. A method for producing a compound as defined in term 12 wherein the leaving group represented by Q2 is a halogen atom, C6-10 arylsulfonyloxy group or a C1-4 alkylsulfonyloxy group,
25. A hydrate of a compound represented by the formula: 
wherein R is a hydrogen atom or an ethyl group, or a succinate or citrate of the compound (Ixe2x80x3),
26. 2-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]imidazo[1,2-b]pyridazin-2-yl]-2-methylpropionic acid dehydrate,
27. A compound as defined in term 26 which shows the following Powder X-ray diffraction analysis result:
28. A compound as defined in term 25 which is {circle around (1)} ethyl 2-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]imidazo[1,2-b]pyridazin-2-yl]-2-methylpropionate disuccinate or {circle around (2)} ethyl 2-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]imidazo[1,2-b]pyridazin-2-yl]-2-methylpropionate citrate,
29. 2-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino)-3-methylimidazo[1,2-b]pyridazin-2-yl)-2-methylpropionic acid or a salt thereof,
30. A pro-drug of a compound as claimed in any one of claims 13 to 11,
31. A method for producing a compound as defined in term which comprises
(1) contacting a compound which is obtained by reacting a compound represented by the formula: 
wherein Q1 is a leaving group, or a salt thereof with a compound represented by the formula: 
wherein Q2 is a leaving group, R is same as defined in claim 13, or a salt thereof with a water, or
(2) reacting a free form of the compound (Ixe2x80x3) as defined in claim 13 with a succinic acid or citric acid,
32. A pharmaceutical composition which comprises any one of compounds as defined in terms 25 to 29 or a pro-drug as defined in term 30,
33. A pharmaceutical composition as defined in term 32 which is an anti-histaminic agent and/or an eosinophil chemotaxis-inhibiting agent,
34. A pharmaceutical composition as defined in term 32 which is an anti-allergic agent,
35. A pharmaceutical composition as defined in term 32 which is an agent for treating or preventing asthma, allergic conjunctivitis, allergic rhinitis, chronic urticaria or atopic dermatitis,
36. A method for suppressing a histamine and/or an eosinophil chemotaxis comprising administering an effective amount of any one of compounds as defined in terms 25 to 29 or a pro-drug as defined in term 30 to mammals,
37. A method for treating or preventing allergic diseases comprising administering an effective amount of any one of compounds as defined in terms 25 to 29 or a pro-drug as defined in term 30 to mammals,
38. A method for treating or preventing asthma, allergic conjunctivitis, allergic rhinitis, chronic urticaria or atopic dermatitis which comprises administering any one of compounds as defined in terms 25 to 29 or a pro-drug as defined in term 30 to mammals,
39. Use of any one of compounds as defined in terms 25 to 29 or a pro-drug as defined in term 30 for preparing a pharmaceutical composition for suppressing a histamine and/or an eosinophil chemotaxis,
40. Use of any one of compounds as defined in terms 25 to 29 or a pro-drug as defined in term 30 for preparing a pharmaceutical composition for treating or preventing allergic diseases, and
41. Use of any one of compounds as defined in terms 25 to 29 or a pro-drug as defined in term 30 for preparing a pharmaceutical composition for treating or preventing asthma, allergic conjunctivitis, allergic rhinitis, chronic urticaria or atopic dermatitis.
And, the present invention provides:
42. An agent for treating or preventing as defined in term 1 wherein Ar1 and Ar2 are independently an aromatic hydrocarbon group which may be substituted,
43. An agent for treating or preventing as defined in term 1 wherein Ar1 and Ar2 are independently a phenyl group which may be substituted,
44. An agent for treating or preventing as defined in term 1 wherein Ar1 and Ar2 are independently (i) a phenyl group which may be substituted by a halogen atom or C1-6 alkyl or (ii) a 5 to 8 membered aromatic heterocyclic group containing 1 to 4 hetero atoms selected from a nitrogen atom, a sulfur atom and an oxygen atom other than carbon atoms,
45. An agent for treating or preventing as defined in term 1 wherein the ring B is a ring represented by the formula: 
wherein Z is a nitrogen atom or a methyne group; Z1 and Z2 are independently a linear C1-4 alkylene group which may be substituted by hydroxy, oxo or C1-6 alkyl,
46. An agent for treating or preventing as defined in term 45 wherein Z1 and Z2 are independently a linear C1-2 alkylene group,
47. An agent for treating or preventing as defined in term 1 wherein X is a bond, an oxygen atom or NH,
48. An agent for treating or preventing as defined in term 1 wherein X is a bond or an oxygen atom,
49. An agent for treating or preventing as defined in term 1 wherein Y is a group represented by the formula:
xe2x80x94(CH2)m-Y1xe2x80x94(CH2)n-Y2xe2x80x94
wherein Y1 and Y2 are the same or different and are independently a bond, an oxygen atom, S(O)p wherein p is an integer of 0 to 2, NR4 wherein R4 is a hydrogen atom or a lower alkyl group, a carbonyl group, a carbonyloxy group or a group represented by the formula: 
wherein R5 and R6 are the same or different and are independently a hydroxy group or a C1-4 alkyl group; m and n are an integer of 0 to 4, and sum of m and n is not more than 6,
50. An agent for treating or preventing as defined in term 1 wherein Y is
(i) a C1-6 alkylene group,
(ii) xe2x80x94(CH2)p1Oxe2x80x94,
(iii) xe2x80x94(CH2)p1NHxe2x80x94,
(iv) xe2x80x94(CH2)p1Sxe2x80x94,
(v) xe2x80x94(CH2)q1CH(OH)(CH2)q2Oxe2x80x94,
(vi) xe2x80x94(CH2)q1CH(OH)(CH2)q2NHxe2x80x94,
(vii) xe2x80x94(CH2)q1CH(OH)(CH2)q2Sxe2x80x94,
(viii) xe2x80x94(CH2)p1CONHxe2x80x94,
(ix) xe2x80x94COO(CH2)p1Oxe2x80x94,
(x) xe2x80x94COO(CH2)p1NHxe2x80x94,
(xi) xe2x80x94COO(CH2)p1Sxe2x80x94,
(xii) xe2x80x94(CH2)q1O(CH2)q2Oxe2x80x94,
(xiii) xe2x80x94(CH2)q1O(CH2)q2NHxe2x80x94 or
(xiv) xe2x80x94(CH2)q1O(CH2)q2Sxe2x80x94 wherein p1 is an integer of 1 to 6, q1 and q2 are an integer of 1 to 3,
51. An agent for treating or preventing as defined in term 1 wherein R1, R2, R3 and R7 are the same or different and are independently (i) a hydrogen atom, (ii) a C1-6 alkyl group which may be substituted by carboxyl or C1-6 alkoxy-carbonyl, (iii) a C1-6 alkoxy group, (iv) a C1-6 alkoxy-carbonyl group or (v) a carboxyl group,
52. An agent for treating or preventing as defined in term 1 wherein R1 is, (i) a hydrogen atom, (ii) a C1-6 alkyl group which may be substituted by carboxyl, C1-6 alkoxy-carbonyl, hydroxy or carbamoyl optionally having mono-or di-C1-6 alkyl, (iii) a C6-14 aryl group, (iv) a C1-6 alkoxy group, (v) a C1-6 alkoxy-carbonyl group, (vi) a carboxyl group, (vii) a carbamoyl group which may be substituted by a C1-6 alkyl group optionally having carboxyl or C1-6 alkoxy-carbonyl or (viii) a C3-6 cycloalkyl group which may be substituted by C1-6 alkoxy-carbonyl,
53. An agent for treating or preventing as defined in term 1 wherein R2 is a hydrogen atom, a C1-6 alkyl group, a C1-6 alkoxy-carbonyl group or a carboxyl group,
54. An agent for treating or preventing as defined in term 1 wherein R3 is a hydrogen atom,
55. An agent for treating or preventing as defined in term 1 wherein R7 is a hydrogen atom, a halogen atom, a C1-6 alkyl group, a C1-6 alkoxy-carbonyl group or a carboxyl group,
56. An agent for treating or preventing as defined in term 1 wherein R8 is a hydrogen atom or a hydroxy group,
57. An agent for treating or preventing as defined in term 1 wherein A is a nitrogen atom,
58. An agent for treating or preventing as defined in term 1 wherein A is CR7xe2x80x2 wherein R7xe2x80x2 is a hydrogen atom, a halogen atom, a C1-6 alkyl group, a C1-6 alkoxy-carbonyl group or a carboxyl group,
59. An agent for treating or preventing as defined in term 1 wherein A is CH,
60. An agent for treating or preventing as defined in term 1 wherein the compound is Ethyl 2-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]imidazo[1,2-b]pyridazin-2-yl]-2-methylpropionate or a salt thereof,
61. An agent for treating or preventing as defined in term 1 wherein the compound is 2-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]imidazo[1,2-b]pyridazin-2-yl]-2-methylpropionic acid or a salt thereof,
62. An agent for treating or preventing as defined in term 1 wherein the compound is Ethyl N-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]imidazo[1,2-b]pyridazine-2-carbonyl]glycinate or a salt thereof,
63. An agent for treating or preventing as defined in term 1 wherein the compound is Ethyl 2-[6-[3-[4-(diphenylmethoxy)piperidino)propylamino]-3-methylimidazo[1,2-b]pyridazin-2-yl]-2-methylpropionate or a salt thereof,
64. An agent for treating or preventing as defined in term 1 wherein the compound is Ethyl 2-[6-[3-[4-(diphenylmethylamino)piperidino]propylamino]imidazo[1,2-b]pyridazin-2-yl]-2-methylpropionate or a salt thereof,
65. An agent for treating or preventing as defined in term 1 wherein the compound is 2-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]-3-methylimidazo[1,2-b]pyridazin-2-yl]-2-methylpropionic acid or a salt thereof,
66. An agent for treating or preventing as defined in term 1 wherein the compound is a hydrate of a compound represented by the formula: 
wherein R is a hydrogen atom or an ethyl group, or a succinate or citrate of the compound (Ixe2x80x3),
67. An agent for treating or preventing as defined in term 1 wherein the compound is ethyl 2-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]imidazo[1,2-b]pyridazin-2-yl]-2-methylpropionate disuccinate,
68. An agent for treating or preventing as defined in term 1 wherein the compound is ethyl 2-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]imidazo[1,2-b]pyridazin-2-yl]-2-methylpropionate citrate,
69. A method as defined in term 13 where in the boiling point of the solvent is about 90xc2x0 C. to about 220xc2x0 C.,
70. A method as defined in term 12 wherein the solvent is ethers, aromatic hydrocarbons, nitriles, cyclic amides, sulfoxides, cyclic sulfones, halogenated hydrocarbons or azoles,
71. A method as defined in term 12 wherein the solvent is dioxane, tetrahydrofuran, benzene, toluene, xylene, acetonitrile, N,N-dimethylformamide, N,N-dimethylacetamide, 1-methyl-2-pyrolidone, dimethyl sulfoxide, sulforane, dichloroethane, chloroform, imidazole, 2-methylimidazole or pyridine,
72. A method as defined in term 12 wherein the solvent is cyclic amides or sulfoxides,
73. A method as defined in term 12 wherein the solvent is 1-methyl-2-pyrolidone, dimethyl sulfoxide or sulforane,
74. A method as defined in term 12 wherein the base is alkali metal hydrides, alkali metal alkoxide, alkali metal hydroxides, alkali metal carbonates, alkali earth metal hydrides, alkali earth metal alkoxide, alkali earth metal hydroxides or alkali earth metal carbonates,
75. A method as defined in term 12 wherein the base is sodium hydride, potassium hydride, sodium methoxide, sodium ethoxide, sodium t-butoxide, sodium hydroxide, potassium hydroxide, lithium carbonate, sodium carbonate or potassium carbonate,
76. A method as defined in term 12 wherein the reaction temperature is about 100xc2x0 C. to about 180xc2x0 C.,
77. A method as defined in term 12 wherein the reaction time is about 30 minutes to about 30 hours,
78. A method as defined in term 12 wherein the reaction is conducted in the presence of magnesium sulfate, zinc chloride, cuprous chloride (CuCl), potassium fluoride or lithium chloride,
79. A method as defined in term 12 wherein an amount of the compound (II) or a salt thereof is at about 1 to about 5 mol to 1 mol of the compound (III) or a salt thereof,
80. A method as defined in term 12 wherein an amount of the compound (II) or a salt thereof is at about 1.0 to about 1.7 mol to 1 mol of the compound (III) or a salt thereof in the presence of the base,
81. A method as defined in term 12 wherein an amount of the compound (II) or a salt thereof is at about 1.5 mol to 1 mol of the compound (III) or a salt thereof in the presence of the base,
82. A method as defined in term 12 wherein the reaction is conducted in an atmosphere of inert gas,
83. A method as defined in term 12 wherein the inert gas is N2 gas or argon gas, 84. A method as defined in term 12 wherein R1xe2x80x2 is a hydrocarbon group substituted by a group represented by the formula: xe2x80x94COOR11 wherein R11 is a hydrogen atom or a hydrocarbon group which may be substituted,
85. A method as defined in term 12 wherein R1xe2x80x2 is a C1-6 alkyl group which may be substituted by carboxyl or C1-6 alkoxy-carbonyl,
86. A method as defined in term 12 wherein R1xe2x80x2 is a carboxyl dimethylmethyl group or C1-6 alkoxy-carbonyl dimethylmethyl group,
87. A method as defined in term 12 wherein R1xe2x80x2 is carboxyl or ethoxycarbonyl,
88. A method as defined in term 12 wherein Ar1xe2x80x2 and Ar2xe2x80x2 are independently a phenyl group which may be substituted by a halogen atom or C1-6 alkyl; the ring Bxe2x80x2 is a ring represented by the formula: 
wherein Z is a nitrogen atom or a methyne group; Z1xe2x80x3 and Z2xe2x80x3 is independently an ethylene group which may be substituted by hydroxy, oxo or C1-6 alkyl; X is a bond, an oxygen atom or NH; Y is
(i) a C1-6 alkylene group,
(ii) xe2x80x94(CH2)p1Oxe2x80x94,
(iii) xe2x80x94(CH2)p1NHxe2x80x94,
(iv) xe2x80x94(CH2)p1Sxe2x80x94,
(v) xe2x80x94(CH2)q1CH(OH)(CH2)q2Oxe2x80x94,
(vi) xe2x80x94(CH2)q1CH(OH)(CH2)q2NHxe2x80x94,
(vii) xe2x80x94(CH2)q1CH(OH)(CH2)q2Sxe2x80x94,
(viii) xe2x80x94(CH2)p1CONHxe2x80x94,
(ix) xe2x80x94COO(CH2)p1Oxe2x80x94,
(x) xe2x80x94COO(CH2)p1NHxe2x80x94,
(xi) xe2x80x94COO(CH2)p1Sxe2x80x94,
(xii) xe2x80x94(CH2)q1O(CH2)q2Oxe2x80x94,
(xiii) xe2x80x94(CH2)q1O(CH2)q2NHxe2x80x94 or
(xiv) xe2x80x94(CH2)q1O(CH2)q2Sxe2x80x94 wherein p1 is an integer of 1 to 6, q1 and q2 are an integer of 1 to 3; A is a nitrogen atom or CR7xe2x80x2 wherein R7xe2x80x2 is a hydrogen atom, a halogen atom, a C1-6 alkyl group, a C1-6 alkoxy-carbonyl group or a carboxyl group; R1xe2x80x2 is a C1-6 alkyl group which may be substituted by carboxyl or C1-6 alkoxy-carbonyl; R2 is a hydrogen atom, a C1-6 alkyl group, a C1-6 alkoxy-carbonyl group or a carboxyl group; R3 is a hydrogen atom; R8 is a hydrogen atom or a hydroxyl group,
89. A method as defined in term 12 wherein Ar1xe2x80x2 and Ar2xe2x80x2 are independently a phenyl group; the ring Bxe2x80x2 is a ring represented by the formula: 

X is an oxygen atom or a bond; Y is xe2x80x94(CH2)p1NHxe2x80x94 wherein p1 is an integer of 1 to 6; A is CR7xe2x80x3 wherein R7xe2x80x3 is a hydrogen atom or a C1-6 alkyl group; R1xe2x80x2 is a C1-6 alkyl group which may be substituted by carboxyl or C1-6 alkoxy-carbonyl; R2 is a hydrogen atom; R3 is a hydrogen atom; R8 is a hydrogen atom,
90. A method as defined in term 23 wherein the alkali metal is lithium, sodium or potassium, and
91. N-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]-3-methylimidazo[1,2-b]pyridazine-2-carbonyl]glycine (thereinafter referred to as compound (Ib)) oa a salt thereof.
And, when the compound (I), (Ixe2x80x2), (Ixe2x80x3) or a salt thereof has asymmetric carbons, the present invention includes stereoisomers or racemates. The compound (I) or a salt thereof may be hydrate or anhydride.
In the above mentioned formula (I), Ar1 and Ar2 are independently an aromatic group which may be substituted, and Ar1 and Ar2 may form a condensed cyclic ring with an adjacent carbon atom.
As the xe2x80x9caromatic groupxe2x80x9d represented by Ar1 and Ar2, for example, {circle around (1)} a single cyclic or condensed cyclic aromatic hydrocarbon group, preferably C6-14 single cyclic or condensed cyclic aromatic hydrocarbon group such as C6-14 aryl group (e.g. phenyl, tolyl, xylyl, biphenyl, 1-naphthyl, 2-naphthyl, 2-indenyl, 1-anthryl, 2-anthryl, 9-anthryl, 1-phenanthryl, 2-phenanthryl, 3-phenanthryl, 4-phenanthryl, 9-phenanthryl, etc.), more preferably phenyl, tolyl, xylyl, biphenyl, 1-naphthyl, 2-naphthyl, particularly phenyl, etc., {circle around (2)} a group removed a hydrogen atom from a single cyclic group (preferably 5 to 8 membered single cyclic group) containing more than 1 (for example 1 to 4, preferably 1 to 3) and one or more than two kinds of hetero atoms selected from a nitrogen atom, a sulfur atom and an oxygen atom other than carbon atoms, or a condensed aromatic heterocyclic group thereof, preferably an aromatic hetero ring removed a hydrogen atom, more specifically an aromatic heterocycle such as thiophene, benzo[b]thiophene, benzo[b]furan, benzimidazole, benzoxazole, benzothiazole, benzisothiazole, naphtho[2,3-b]thiophene, thianthrene, furan, indolylzine, xanthene, phenoxathlin, pyrrole, imidazole, triazole, thiazole, oxazole, pyrazole, pyridine, pyrazine, pyrimidine, pyridazine, indole, isoindole, 1H-indazole, purine, 4H-quinolizine, isoquinoline, quinoline, phthalazine, naphthylidine, quinoxaline, quinazoline, cinnoline, carbazole, xcex2-carboline, phenanthridine, acridine, phenazine, isothiazole, phenothiazine, isoxazole, furaxan, phenoxazine or isochroman, preferably pyridine, thiophene, furan, more preferably pyridine, or a condensed ring formed by these rings (preferably the single ring as mentioned above) and one or few (preferably 1 or 2, more preferably 1) aromatic ring (for example the above mentioned aromatic hydrocarbon group, more preferably benzene ring, etc.), etc. are used.
As the xe2x80x9caromatic group of the aromatic group optionally having a substituentxe2x80x9d represented by Ar1 and Ar2 for example, phenyl, etc. are preferable.
As the xe2x80x9csubstituentsxe2x80x9d of the xe2x80x9caromatic groupxe2x80x9d represented by Ar1 and Ar2, for example,
(i) a halogen atom (e.g. fluorine, chlorine, bromine, iodine),
(ii) a lower alkylenedioxy group (e.g. C1-3 alkylenedioxy such as methylenedioxy, ethylenedioxy),
(iii) a nitro group,
(iv) a cyano group,
(v) an optionally halogenated lower alkyl group,
(vi) an optionally halogenated lower alkenyl group,
(vii) an optionally halogenated lower alkynyl group,
(viii) a lower cycloalkyl group (e.g. C3-6 cycloalkyl such as cyclopropyl, cyclobutyl, cyclopenthyl, cyclohexyl),
(ix) an optionally substituted lower alkoxy group,
(x) an optionally halogenated lower alkylthio group,
(xi) a hydroxy group,
(xii) an amino group,
(xiii) a mono-lower alkylamino group (e.g. mono-C1-6 alkylamino such as methylamino, ethylamino, propylamino, isopropylamino, butylamino),
(xiv) a di-lower alkylamino group (e.g. di-C1-6 alkylamino such as dimethylamino, diethylamino, dipropylamino, dibutylamino),
(xv) a 5 or 6 membered cyclic amino group (e.g. morpholino, piperazin-1-yl, piperidino, pyrrolidin-1-yl),
(xvi) a lower alkylcarbonyl group (e.g. C1-6 alkylcarbonyl such as acetyl, propionyl),
(xvii) a carboxyl group,
(xviii) a lower alkoxy-carbonyl group (e.g. C1-6 alkoxy-carbonyl such as methoxycarbonyl, ethoxycarbonyl, propoxycarbonyl, butoxycarbonyl),
(xix) a carbamoyl group,
(xx) a thiocarbamoyl group,
(xxi) a mono-lower alkyl-carbamoyl group (e.g. N-mono-C1-6 alkyl-carbamoyl such as methylcarbamoyl, ethylcarbamoyl),
(xxii) a di-lower alkyl-carbamoyl group (e.g. di-C1-6 alkyl-carbamoyl such as dimethylcarbamoyl, diethylcarbamoyl),
(xxiii) aryl-carbamoyl (e.g. C6-10 aryl-carbamoyl such as phenylcarbamoyl, naphthylcarbamoyl),
(xxiv) a sulfo group,
(xxv) a lower alkyl sulfonyl group (e.g. C1-6 alkyl sulfonyl such as methylsulfonyl, ethylsulfonyl),
(xxvi) an aryl group (e.g. C6-10 aryl such as phenyl, naphthyl) or
(xxvii) an aryloxy group (e.g. C6-10 aryloxy such as phenyloxy, naphthyloxy),
(xxviii) an aralkyloxy group (e.g. C7-16 aralkyloxy such as benzyloxy), etc. are used.
As the xe2x80x9coptionally halogenated lower alkyl groupxe2x80x9d, for example, a lower alkyl group (e.g. C1-6 alkyl such as methyl, ethyl, propyl, isopropyl, butyl, isobutyl, sec-butyl, tert-butyl, pentyl, hexyl) optionally substituted by 1 to 3 halogen atoms (e.g. fluorine, chlorine, bromine, iodine), etc. are exemplified. As specific examples, for example, methyl, fluoromethyl, chloromethyl, difluoromethyl, trichloromethyl, trifluoromethyl, ethyl, 2-bromoethyl, 2,2,2-trifluoroethyl, propyl, 3,3,3-trifluoropropyl, isopropyl, butyl, 4,4,4-trifluorobutyl, isobutyl, sec-butyl, tert-butyl, pentyl, isopentyl, neopentyl, 5,5,5-trifluoropentyl, hexyl, 6,6,6-trifluorohexyl, etc. are used.
As the xe2x80x9coptionally halogenated lower alkenyl groupxe2x80x9d, for example, a lower alkenyl group and the xe2x80x9coptionally halogenated lower alkynyl groupxe2x80x9d, for example, a lower alkenyl group (e.g., a C2-6 alkenyl group such as vinyl, propenyl, isopropenyl, 2-buten-1-yl, 4-penten-1-yl, 5-hexen-1-yl, etc.) optionally substituted by 1 to 3 halogen atoms (e.g. fluorine, chlorine, bromine, iodine) and a lower alkynyl group (e.g., a C2-6 alkynyl group such as 2-butyn-1-yl, 4-pentyn-1-yl, 5-hexyn-1-yl, etc.) optionally substituted by 1 to 3 halogen atoms (e.g. fluorine, chlorine, bromine, iodine), etc. are used.
As the xe2x80x9coptionally substituted lower alkoxy groupxe2x80x9d, for example, a lower alkoxy group (e.g. a C1-6 alkoxy group such as methoxy, ethoxy, propoxy, isopropoxy, n-butoxy, isobutoxy, sec-butoxy, tert-butoxy, etc.) optionally substituted by 1 to 3 halogen atoms (e.g. fluorine, chlorine, bromine, iodine), mono- or di-lower alkylamino groups (e.g. mono- or di-C1-6 alkylamino such as methylamino, dimethylamino, ethylamino, dimethylamino) or lower alkoxy-carbonyl groups (e.g. C1-6 alkoxy-carbonyl such as methoxycarbonyl, ethoxycarbonyl), etc. are used.
As the xe2x80x9coptionally halogenated lower alkylthio groupxe2x80x9d, for example, a lower alkylthio group (e.g. a C1-6 alkylthio group such as methylthio, ethylthio, n-propylthio, isopropylthio, n-butylthio, isobutylthio, sec-butylthio, tert-butylthio) optionally substituted by 1 to 3 halogen atoms (e.g. fluorine, chlorine, bromine, iodine), etc. are used, and as specific examples, methylthio, difluoromethylthio, trifluoromethylthio, ethylthio, propylthio, isopropylthio, butylthio, 4,4,4-trifluorobutylthio, pentylthio, hexylthio, etc. are used.
As specific examples of the condensed ring formed by Ar1, Ar2 and the adjacent carbon atom, for example, a condensed ring represented by the formula: 
wherein R8 is same as defined above, etc. are used.
As Ar1 and Ar2, same or different and independently, an aromatic hydrocarbon group (preferably C6-14 aromatic hydrocarbon group) which may be substituted is preferable, and a benzene ring which may be substituted is more preferable. More specifically, as Ar1 and Ar2, independently, (1) a phenyl group which may be substituted by a halogen atom or C1-6 alkyl or (2) a 5 to 8 membered aromatic heterocyclic group containing 1 to 4 hetero atoms selected from a nitrogen atom, a sulfur atom and an oxygen atom other than carbon atoms, etc. are preferable.
In the above mentioned formula (I), the ring B represents a xe2x80x9cnitrogen-containing heterocycle optionally having a substituentxe2x80x9d, provided that the ring B is not a heterocycle represented by the formula: 
wherein n is 0 or 1.
As the xe2x80x9cnitrogen-containing heterocyclexe2x80x9d represented by the ring B, for example, a 3 to 13 membered nitrogen-containing heterocycle containing at least one nitrogen atom which may contain 1 to 3 hetero atoms selected w from a nitrogen atom, an oxygen atom and a sulfur atom, etc. are used. In the above mentioned formula (I), it is preferable that a bivalent group removed one hydrogen atom from the nitrogen atom and others atom of the ring B, respectively, is formed. Specifically, a 3 to 9 membered (preferably 3 to 6 membered) nitrogen atom-containing heterocyclic group such as 
etc. are preferable.
As the substituents of the nitrogen atom-containing heterocycle represented by the ring B, for example, an oxo group as well as the xe2x80x9csubstituentsxe2x80x9d of the xe2x80x9caromatic group optionally having a substituentxe2x80x9d represented by Ar1 and Ar2, etc. are used.
As preferable specific examples of the ring B, for example, a ring represented by the formula: 
wherein Z is a nitrogen atom or a methyne group, Z1 and Z2 are independently a linear C1-4 alkylene group which may be substituted by a hydroxy group, an oxo group or a C1-6 alkyl group, etc. are used.
As the xe2x80x9cC1-6 alkyl groupxe2x80x9d, for example, a linear or branched C1-6 alkyl group such as methyl, ethyl, propyl, isopropyl, butyl, isobutyl, sec-butyl, tert-butyl, pentyl, hexyl, etc. are used.
As the xe2x80x9clinear C1-4 alkylene groupxe2x80x9d, for example, a linear C1-4 alkylene group such as methylene, ethylene, propylene, butylene, etc. are used.
As the xe2x80x9clinear C1-4 alkylene group which may be substituted by a hydroxy group, an oxo group or a C1-6 alkyl groupxe2x80x9d represented by Z1 and Z2, an unsubstituted linear C1-4 alkylene group, etc. are used, and particularly, an unsubstituted linear C1-2 alkylene group is preferable.
As more preferable ring B, piperidine, piperazine, etc. are exemplified.
In the above mentioned formula (I), X and Y are the same or different and are independently {circle around (1)} a bond, {circle around (2)} an oxygen atom, {circle around (3)} S(O)p (p is an integer of 0 to 2), {circle around (4)} NR4 wherein R4 is a hydrogen atom or a lower alkyl group or {circle around (5)} a bivalent linear lower hydrocarbon group which may contain 1 to 3 hetero atoms and the bivalent linear lower hydrocarbon group may have substituents.
As the lower alkyl group represented by R4, for example, a linear or branched C1-6 alkyl group such as methyl, ethyl, propyl, isopropyl, butyl, isobutyl, sec-butyl, tert-butyl, pentyl, hexyl, etc. are used.
As the xe2x80x9cbivalent linear lower hydrocarbon group which may contain 1 to 3 hetero atomsxe2x80x9d represented by X and Y, for example, a group which is formed by removing each one hydrogen atom (sum two hydrogen atoms) bonded to same or different carbon atom from a lower (C1-6)hydrocarbon, and which may optionally contain hetero atoms selected from an oxygen atom and a sulfur atom in the hydrocarbon chain is exemplified.
As specific examples of the xe2x80x9cbivalent linear lower hydrocarbon groupxe2x80x9d, for example,
(i) a C1-6 alkylene group (e.g., xe2x80x94CH2xe2x80x94, xe2x80x94(CH2)2xe2x80x94, xe2x80x94(CH2)3xe2x80x94, xe2x80x94(CH2)4xe2x80x94, xe2x80x94(CH2)5xe2x80x94, xe2x80x94(CH2)6xe2x80x94, etc.)
(ii) a C2-6 alkenylene group (e.g., xe2x80x94CHxe2x95x90CHxe2x80x94, xe2x80x94CHxe2x95x90CHxe2x80x94CH2xe2x80x94, xe2x80x94CH2xe2x80x94CHxe2x95x90CHxe2x80x94CH2xe2x80x94, xe2x80x94(CH2)2xe2x80x94CHxe2x95x90CHxe2x80x94CH2xe2x80x94, xe2x80x94(CH2)2xe2x80x94CHxe2x95x90CHxe2x80x94(CH2)2xe2x80x94, xe2x80x94(CH2)3xe2x80x94CHxe2x95x90CHxe2x80x94CH2xe2x80x94, etc.),
(iii) a C2-6 alkynylene group (e.g., xe2x80x94Cxe2x89xa1Cxe2x80x94, xe2x80x94Cxe2x89xa1Cxe2x80x94CH2xe2x80x94, xe2x80x94CHxe2x80x94Cxe2x89xa1Cxe2x80x94CH2xe2x80x94, xe2x80x94(CH2)2xe2x80x94Cxe2x89xa1Cxe2x80x94CH2xe2x80x94, xe2x80x94(CH2)2xe2x80x94Cxe2x89xa1Cxe2x80x94(CH2)2xe2x80x94, xe2x80x94(CH2)3xe2x80x94Cxe2x89xa1Cxe2x80x94CH2xe2x80x94, etc.), etc. are used.
As the xe2x80x9csubstituentsxe2x80x9d of the xe2x80x9cbivalent linear lower hydrocarbon group which may contain 1 to 3 hetero atomsxe2x80x9d represented by X and Y, an oxo group as well as the xe2x80x9csubstituentsxe2x80x9d of the xe2x80x9caromatic group optionally having a substituentxe2x80x9d represented by the above mentioned Ar1 and Ar2, etc. are used, and a hydroxy group or an oxo group is preferable.
As X, a bond, an oxygen atom or NH is preferable, and particularly, a bond or an oxygen atom is preferable.
As Y, for example, a group represented by the formula:
xe2x80x94(CH2)m-Y1xe2x80x94(CH2)n-Y2xe2x80x94
wherein Y1 and Y2 are the same or different and are independently a bond, an oxygen atom, S(O)p wherein p is same as defined above, NR4 wherein R4 is same as defined above, a carbonyl group, a carbonyloxy group or a group represented by the formula: 
wherein R5 and R6 are the same or different and are independently a hydroxy group or a C1-4 alkyl group; m and n are independently an integer of 0 to 4, (provised that, sum of m and n is not more than 6), etc. are used.
As the xe2x80x9cC1-4 alkyl groupxe2x80x9d represented by R5 and R6, for example, a linear or branched C1-4 alkyl group such as methyl, ethyl, propyl, isopropyl, butyl, isobutyl, sec-butyl, tert-butyl, etc. are used.
As Y, for example, a group represented by
(i) a C1-6 alkylene group,
(ii) xe2x80x94(CH2)p1Oxe2x80x94,
(iii) xe2x80x94(CH2)p1NHxe2x80x94,
(iv) xe2x80x94(CH2)p1Sxe2x80x94,
(v) xe2x80x94(CH2)q1CH(OH)(CH2)q2Oxe2x80x94,
(vi) xe2x80x94(CH2)q1CH(OH)(CH2)q2NHxe2x80x94,
(vii) xe2x80x94(CH2)q1CH(OH)(CH2)q2Sxe2x80x94,
(viii) xe2x80x94(CH2)p1CONHxe2x80x94,
(ix) xe2x80x94COO(CH2)p1Oxe2x80x94,
(x) xe2x80x94COO(CH2)p1NHxe2x80x94,
(xi) xe2x80x94COO(CH2)p1Sxe2x80x94,
(xii) xe2x80x94(CH2)q1O(CH2)q2Oxe2x80x94,
(xiii) xe2x80x94(CH2)q1O(CH2)q2NHxe2x80x94 or
(xiv) xe2x80x94(CH2)q1O(CH2)q2Sxe2x80x94 wherein p1 is an integer of 1 to 6, q1 and q2 are an integer of 1 to 3, etc. are preferable.
Of them, as Y, a bond, xe2x80x94(CH2)2xe2x80x94Oxe2x80x94, xe2x80x94(CH2)3xe2x80x94Oxe2x80x94, xe2x80x94(CH2)4xe2x80x94Oxe2x80x94, xe2x80x94(CH2)6xe2x80x94Oxe2x80x94, xe2x80x94(CH2)2xe2x80x94NHxe2x80x94, xe2x80x94(CH2)3xe2x80x94NHxe2x80x94, xe2x80x94(CH2)4xe2x80x94NHxe2x80x94, xe2x80x94(CH2)3xe2x80x94Sxe2x80x94, xe2x80x94CH2xe2x80x94CH(OH)xe2x80x94CH2xe2x80x94Oxe2x80x94, xe2x80x94(CH2)2xe2x80x94COxe2x80x94NHxe2x80x94, xe2x80x94CH2xe2x80x94COxe2x80x94NHxe2x80x94, xe2x80x94COxe2x80x94Oxe2x80x94(CH2)2xe2x80x94Oxe2x80x94, xe2x80x94COxe2x80x94Oxe2x80x94(CH2)3xe2x80x94Oxe2x80x94, xe2x80x94(CH2)6xe2x80x94NHxe2x80x94, xe2x80x94(CH2)6xe2x80x94Sxe2x80x94, xe2x80x94(CH2)2xe2x80x94Oxe2x80x94(CH2)2xe2x80x94Oxe2x80x94, xe2x80x94(CH2)2xe2x80x94Oxe2x80x94(CH2)2xe2x80x94Sxe2x80x94, etc. are preferable.
In the above mentioned formula (I) A is a nitrogen atom or CR7 wherein R7 is a hydrogen atom, a halogen atom, a hydrocarbon group which may be substituted, an acyl group or a hydroxy group which may be substituted.
As the xe2x80x9chalogen atomxe2x80x9d represented by R7, fluorine, chlorine, bromine, iodine are exemplified.
As the xe2x80x9chydrocarbon groupxe2x80x9d represented by R7, for example, a group removed one hydrogen atom from the hydrocarbon compound is exemplified, and as the specific examples, a linear and cyclic hydrocarbon group such as alkyl group, alkenyl group, alkynyl group, cycloalkyl group, aryl group, aralkyl group, etc. are exemplified. Of them, a C1-16 chain (linear or branched) or cyclic hydrocarbon group, etc. are preferable, and
(a) an alkyl group, preferably lower alkyl group (e.g. a C1-6 alkyl group such as methyl, ethyl, propyl, isopropyl, butyl, isobutyl, sec-butyl, tert-butyl, pentyl, hexyl, etc.),
(b) an alkenyl group, preferably lower alkenyl group (e.g. a C2-6 alkenyl such as vinyl, allyl, isopropenyl, butenyl, isobutenyl, sec-butenyl, etc.),
(c) an alkynyl group, preferably lower alkynyl (e.g. a C2-6 alkynyl such as propargyl, ethynyl, butynyl, 1-hexynyl, etc.),
(d) a cycloalkyl group, preferably lower cycloalkyl (e.g. a C3-6 cycloalkyl such as cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl which may condense with a benzene ring optionally having 1 to 3 lower alkoxys (e.g. a C1-6 alkoxy group such as methoxy), etc.),
(e) an aryl group (e.g. C6-14 aryl group such as phenyl, tolyl, xylyl, biphenyl, 1-naphthyl, 2-naphthyl, 2-indenyl, 1-anthryl, 2-anthryl, 9-anthryl, 1-phenanthryl, 2-phenanthryl, 3-phenanthryl, 4-phenanthryl or 9-phenanthryl, etc., preferably phenyl),
(f) an aralkyl group (e.g. a C7-16 aralkyl group such as benzyl, phenethyl, diphenylmethyl, 1-naphthylmethyl, 2-naphthylmethyl, 2-phenylethyl, 2-diphenylethyl, 1-phenylpropyl, 2-phenylpropyl, 3-phenylpropyl, 4-phenylbutyl or 5-phenylpentyl, etc., preferably benzyl).
As the xe2x80x9csubstituentsxe2x80x9d of the xe2x80x9chydrocarbon groupxe2x80x9d represented by R7, for example, an oxo group as well as the xe2x80x9csubstituentsxe2x80x9d of the xe2x80x9caromatic group optionally having a substituentxe2x80x9d represented by the above mentioned Ar1 and Ar2, etc. are used.
As the xe2x80x9cacyl groupxe2x80x9d represented by R7, for example, xe2x80x94(Cxe2x95x90O)xe2x80x94R9, xe2x80x94SO2xe2x80x94R9, xe2x80x94SOxe2x80x94R9, xe2x80x94(Cxe2x95x90O)NR10R9, xe2x80x94(Cxe2x95x90O)Oxe2x80x94R9, xe2x80x94(Cxe2x95x90S)Oxe2x80x94R9 or xe2x80x94(Cxe2x95x90S)NR10OR9 wherein R9 is a hydrogen atom, a hydrocarbon group optionally having a substituent or a hydroxy group optionally having a substituent; and R10 is a hydrogen atom or a lower alkyl group (e.g., a C1-6 alkyl group such as methyl, ethyl, propyl, isopropyl, butyl, isobutyl, sec-butyl, tert-butyl, pentyl, hexyl, etc. and preferably a C1-3 alkyl such as methyl, ethyl, propyl, isopropyl, etc.), etc. are exemplified.
Of them, xe2x80x94(Cxe2x95x90O)xe2x80x94R9, xe2x80x94SO2xe2x80x94R9, xe2x80x94SOxe2x80x94R9, xe2x80x94(Cxe2x95x90O)NR10OR9, xe2x80x94(Cxe2x95x90O)Oxe2x80x94R9 are preferred, and xe2x80x94(Cxe2x95x90O)xe2x80x94R9 is more preferred.
The xe2x80x9chydrocarbon groupxe2x80x9d represented by R9 represents a group having one hydrogen atom removed from the hydrocarbon compound, and as the example, for example, a chained (linear or branched) or cyclic hydrocarbon group such as alkyl group, alkenyl group, alkynyl group, cycloalkyl group, aryl group, aralkyl group, etc. are exemplified, and specifically, the xe2x80x9chydrocarbon groupxe2x80x9d represented by the above mentioned R7, etc. are exemplified, and of them, a C1-6 linear or cyclic hydrocarbon group, etc. are preferable, and particularly a lower (C1-6)alkyl group, etc. are preferable.
As the xe2x80x9csubstituentsxe2x80x9d of the xe2x80x9chydrocarbon groupxe2x80x9d represented by R9, for example, an oxo group as well as the xe2x80x9csubstituentsxe2x80x9d of the xe2x80x9caromatic group optionally having a substituentxe2x80x9d represented by the above mentioned Ar1 and Ar2, etc. are used.
As the xe2x80x9chydroxy group optionally having a substituentxe2x80x9d represented by R9, for example, same those as the xe2x80x9chydroxy group optionally having a substituentxe2x80x9d represented by R7 as mentioned below, etc. are used.
The xe2x80x9chydroxy group optionally having a substituentxe2x80x9d represented by R7 represents (1) a hydroxy group or (2) a hydroxy group having one group such as the above mentioned xe2x80x9chydrocarbon group optionally having a substituentxe2x80x9d instead of a hydrogen atom of the hydroxy group.
As R7, for example, (1) a hydrogen atom, (2) a C1-6 alkyl group which may be substituted by a carboxyl group or C1-6 alkoxy-carbonyl, (3) a C1-6 alkoxy group, (4) a C1-6 alkoxy-carbonyl group, (5) a carboxyl group, etc. are preferable, and particularly a hydrogen atom, a halogen atom, a C1-6 alkyl group, a C1-6 alkoxy-carbonyl group and a carboxyl group are preferable.
As A, a nitrogen atom, CR7xe2x80x2 wherein R7xe2x80x2 is a hydrogen atom, a halogen atom, a C1-6 alkyl group, a C1-6 alkoxy-carbonyl group or a carboxyl group is preferable, and of them, a nitrogen atom, CH or Cxe2x80x94CH3 is preferable, particularly a nitrogen atom or CH is preferable.
In the above mentioned formula (I), R1, R2 and R3 are the same or different and are independently a hydrogen atom, a halogen atom, a hydrocarbon group optionally having a substituent, an acyl group or a hydroxy group optionally having a substituent.
As the xe2x80x9chalogen atomxe2x80x9d represented by R1, R2 and R3, fluorine, chlorine, bromine, iodine are exemplified.
As the xe2x80x9chydrocarbon group optionally having a substituentxe2x80x9d represented by R1, R2 and R3, for example, the xe2x80x9chydrocarbon, group optionally having a substituentxe2x80x9d represented by the above mentioned R1, etc. are used.
As the xe2x80x9cacyl groupxe2x80x9d represented by R1, R2 and R3, for example, the xe2x80x9cacyl groupxe2x80x9d represented by the above mentioned R7, etc. are used.
As the xe2x80x9chydroxy group optionally having a substituentxe2x80x9d represented by R1, R2 and R3, for example, the xe2x80x9chydroxy group optionally having a substituentxe2x80x9d represented by R7, etc. may be used.
As R1, R2and R3, same or different and independently, (1) a hydrogen atom, (2) a C1-6 alkyl group which may be substituted by carboxyl or C1-6 alkoxy-carbonyl, (3) a C1-6 alkoxy group, (4) a C1-6 alkoxy-carbonyl group, (5) a carboxyl group or (6) a C6-14 aryl group (preferably phenyl) is preferable, and (1) a hydrogen atom, (2) a C1-6 alkyl group which may be substituted by carboxyl or C1-6 alkoxy-carbonyl, (3) a C1-6 alkoxy group, (4) a C1-6 alkoxy-carbonyl group or (5) a carboxyl group is more preferable.
And, as R1, (1) a hydrogen atom, (2) a C1-6 alkyl group which may be substituted by a group selected from the group consisting of carboxyl, C1-6 alkoxy-carbonyl, hydroxy or carbamoyl optionally having mono- or di-C1-6 alkyl, (3) a C6-14 aryl group, (4) a C1-6 alkoxy group, (5) a C1-6 alkoxy-carbonyl group, (6) a carboxyl group, (7) a carbamoyl group optionally having C1-6 alkyl which may be substituted by carboxyl or C1-6 alkoxy-carbonyl or (8) a C3-6 cycloalkyl group which may be substituted by C1-6 alkoxy-carbonyl, etc. are also preferable.
As R2, a hydrogen atom, a C1-6 alkyl group, a C1-6 alkoxy-carbonyl group or a carboxyl group is preferable.
As R3, a hydrogen atom is preferable.
In the above mentioned formula (I), R8 represents a hydrogen atom or a hydroxy group which may be substituted by lower alkyl.
In the above mentioned formula (I), as the xe2x80x9clower alkyl groupxe2x80x9d of the xe2x80x9chydroxy group which may be substituted by a lower alkyl groupxe2x80x9d represented by R8, for example, a C1-6 alkyl group such as methyl, ethyl, propyl, isopropyl, butyl, isobutyl, sec-butyl, tert-butyl, pentyl, hexyl, etc. are used.
As R8, a hydrogen atom or a hydroxyl group is preferable, and particularly a hydrogen atom is preferable.
As the compound (I) of the present invention, a compound wherein Ar1 and Ar2 are independently (1) a phenyl group which may be substituted by a halogen atom or C1-6 alkyl or (2) a 5 to 8 membered aromatic heterocyclic group containing 1 to 4 hetero atoms selected from a nitrogen atom, a sulfur atom and an oxygen atom other than carbon atoms; the ring B is a ring represented by the formula: 
wherein Z is a nitrogen atom or a methyne group; Z1 and Z2 is independently a linear C1-4 alkylene group which may be substituted by a hydroxy group, an oxo group or a C1-6 alkyl group; X is a bond, an oxygen atom or NH; Y is a group represented by
(i) a C1-6 alkylene group,
(ii) xe2x80x94(CH2)p1Oxe2x80x94,
(iii) xe2x80x94(CH2)p1NHxe2x80x94,
(iv) xe2x80x94(CH2)p1Sxe2x80x94,
(v) xe2x80x94(CH2)q1CH(OH)(CH2)q2Oxe2x80x94,
(vi) xe2x80x94(CH2)q1CH(OH)(CH2)q2NHxe2x80x94,
(vii) xe2x80x94(CH2)q1CH(OH)(CH2)q2Sxe2x80x94,
(viii) xe2x80x94(CH2)p1CONHxe2x80x94,
(ix) xe2x80x94COO (CH2)p1Oxe2x80x94,
(x) xe2x80x94COO(CH2)p1NHxe2x80x94,
(xi) xe2x80x94COO(CH2)p1Sxe2x80x94,
(xii) xe2x80x94(CH2)q1O(CH2)q2Oxe2x80x94,
(xiii) xe2x80x94(CH2)q1O(CH2)q2NHxe2x80x94 or
(xiv) xe2x80x94(CH2)q1O(CH2)q2Sxe2x80x94 wherein p1 is an integer of 1 to 6, q1 and q2 are an integer of 1 to 3; A is a nitrogen atom or CR7xe2x80x2 wherein R7xe2x80x2 is a hydrogen atom, a halogen atom, a C1-6 alkyl group, a C1-6 alkoxy-carbonyl group or a carboxyl group; R1 is (1) a hydrogen atom, (2) a C1-6 alkyl group which maybe substituted by (i) carboxyl, (ii) C1-6 alkoxy-carbonyl, (iii) hydroxy or (iv) carbamoyl optionally having mono- or di-C1-6 alkyl, (3) a C6-14 aryl group, (4) a C1-6 alkoxy group, (5) a C1-6 alkoxy-carbonyl group, (6) a carboxyl group, (7) a carbamoyl group optionally having C1-6 alkyl which may be substituted by carboxyl or C1-6 alkoxy-carbonyl or (8) a C3-6 cycloalkyl group which may be substituted by C1-6 alkoxy-carbonyl; R2 is a hydrogen atom, a C1-6 alkyl group, a C1-6 alkoxy-carbonyl group or a carboxyl group; R3 is a hydrogen atom; R8 is a hydrogen atom or a hydroxyl group, is preferable.
Particularly, a compound wherein Ar1 and Ar2 are a phenyl group; the ring B is a ring represented by the formula: 
wherein Z is a methyne group; Z1xe2x80x2 and Z2xe2x80x2 are a methylene group or an ethylene group (preferably, an ethylene group); X is a bond, an oxygen atom or NH (preferably, a bond or an oxygen atom); Y is xe2x80x94(CH2)p1NHxe2x80x94 wherein p is an integer of 1 to 6; A is CR7xe2x80x3 wherein R7xe2x80x3 is a hydrogen atom or a C1-6 alkyl group; R1 is (1) a hydrogen atom, (2) a C1-6 alkyl group which may be substituted by carboxyl or C1-6 alkoxy-carbonyl or (3) a carbamoyl group optionally having C1-6 alkyl which may be substituted by C1-6 alkoxy-carbonyl; R2 is a hydrogen atom; R3 is a hydrogen atom; R8 is a hydrogen atom, is more preferable.
More specifically,
(i) Ethyl 2-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]imidazo[1,2-b]pyridazin-2-yl]-2-methylpropionate or a salt thereof (particularly, a difumarate thereof, a disuccinate thereof or a citrate thereof),
(ii) 2-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]imidazo[1,2-b]pyridazin-2-yl]-2-methylpropionic acid or a salt thereof (particularly, a dehydrate thereof),
(iii) Ethyl N-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]imidazo[1,2-b]pyridazine-2-carbonyl]glycinate or a salt thereof,
(iv) Ethyl 2-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]-3-methylimidazo,[1,2-b]pyridazin-2-yl]-2-methylpropionate or a salt thereof (particularly, a dihydrochloride thereof),
(v) Ethyl 2-[6-[3-[4-(diphenylmethylamino)piperidino]propylamino]imidazo[1,2-b]pyridazin-2-yl]-2-methylpropionate or a salt thereof,
(vi) 2-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]-3-methylimidazo[1,2-b]pyridazin-2-yl]-2-methylpropionic acid or a salt thereof, and
(vii) N-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino)-3-methylimidazo[1,2-b]pyridazine-2-carbonyl]glycine or a salt thereof, etc. are preferable.
In the above mentioned formula, Ar1xe2x80x2 and Ar2xe2x80x2 represents an aromatic group optionally having a substituent, and Ar1xe2x80x2 and Ar2xe2x80x2 may form a condensed cyclic ring with an adjacent carbon atom.
As the aromatic group represented by Ar1xe2x80x2 and Ar2, for example, a single cyclic or condensed cyclic aromatic hydrocarbon group is used. Specifically, a C6-14 single cyclic or condensed cyclic aromatic hydrocarbon group such as a C6-14 aryl group such as phenyl, tolyl, xylyl, biphenyl, 1-naphthyl, 2-naphthyl, 2-indenyl, 1-anthryl, 2-anthryl, 9-anthryl, 1-phenanthryl, 2-phenanthryl, 3-phenanthryl, 4-phenanthryl, 9-phenanthryl, etc. (more preferably phenyl, tolyl, xylyl, biphenyl, 1-naphthyl, 2-naphthyl, particularly phenyl, etc.), etc. are used.
As the aromatic ring represented by Ar1xe2x80x2 and Ar2xe2x80x2, for example, a C6-14 aryl group such as phenyl, etc. are preferable.
As the substituents of the aromatic ring represented by Ar1xe2x80x2 and Ar2xe2x80x2, for example,
(i) a halogen atom (e.g. fluorine, chlorine, bromine, iodine),
(ii) a lower alkylenedioxy group (e.g. C1-3 alkylenedioxy such as methylenedioxy, ethylenedioxy),
(iii) a nitro group,
(iv) a cyano group,
(v) an optionally halogenated lower alkyl group,
(vi) an optionally halogenated lower alkenyl group,
(vii) an optionally halogenated lower alkynyl group,
(viii) a lower cycloalkyl group (e.g. C3-6 cycloalkyl such as cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl),
(ix) an optionally substituted lower alkoxy group,
(x) an optionally halogenated lower alkylthio group,
(xi) a hydroxy group,
(xii) an amino group,
(xiii) a mono-lower alkylamino group (e.g. mono-C1-6 alkylamino such as methylamino, ethylamino, propylamino, isopropylamino, butylamino),
(xiv) a di-lower alkylamino group (e.g. di-C1-4 alkylamino such as dimethylamino, diethylamino, dipropylamino, dibutylamino),
(xv) a 5 or 6 membered cyclic amino group (e.g. morpholino, piperazin-1-yl, piperidino, pyrrolidin-1-yl),
(xvi) a lower alkylcarbonyl group (e.g. C1-6 alkylcarbonyl such as acetyl, propionyl),
(xvii) a carboxyl group,
(xviii) a lower alkoxy-carbonyl group (e.g. C1-6 alkoxy-carbonyl such as methoxycarbonyl, ethoxycarbonyl, propoxycarbonyl, butoxycarbonyl),
(xix) a carbamoyl group,
(xx) a thiocarbamoyl group,
(xxi) a mono-lower alkyl-carbamoyl group (e.g. mono-C1-6 alkyl-carbamoyl such as methylcarbamoyl, ethylcarbamoyl),
(xxii) a di-lower alkyl-carbamoyl group (e.g. di-C1-6 alkyl-carbamoyl such as dimethylcarbamoyl, diethylcarbamoyl),
(xxiii) aryl-carbamoyl (e.g. C6-10 aryl-carbamoyl such as phenylcarbamoyl, naphthylcarbamoyl),
(xxiv) a sulfo group,
(xxv) a lower alkyl sulfonyl group (e.g. C1-6 alkyl sulfonyl such as methylsulfonyl, ethylsulfonyl),
(xxvi) an aryl group (e.g. C6-10 aryl such as phenyl, naphthyl),
(xxvii) an aryloxy group (e.g. C6-10 aryloxy such as phenyloxy, naphthyloxy),
(xxviii) an aralkyloxy group (e.g. C7-16 aralkyloxy such as benzyloxy),
(xxviv) an oxo group, etc. are used.
As the xe2x80x9coptionally halogenated lower alkyl groupxe2x80x9d, for example, a lower alkyl group (e.g. a C1-6 alkyl group such as methyl, ethyl, propyl, isopropyl, butyl, isobutyl, sec-butyl, tert-butyl, pentyl, hexyl) optionally substituted by 1 to 3 halogen atoms (e.g. fluorine, chlorine, bromine, iodine), etc. are exemplified, and as specific examples, methyl, fluoromethyl, chloromethyl, difluoromethyl, trichloromethyl, trifluoromethyl, ethyl, 2-bromoethyl, 2,2,2-trifluoroethyl, propyl, 3,3,3-trifluoropropyl, isopropyl, butyl, 4,4,4-trifluorobutyl, isobutyl, sec-butyl, tert-butyl, pentyl, isopentyl, neopentyl, 5,5,5-trifluoropentyl, hexyl, 6,6,6-trifluorohexyl, etc. are used.
As the xe2x80x9coptionally halogenated lower alkenyl groupxe2x80x9d and xe2x80x9coptionally halogenated lower alkynyl groupxe2x80x9d, for example, a lower alkenyl group (e.g. a C2-6 alkenyl group such as vinyl, propenyl, isopropenyl, 2-buten-1-yl, 4-penten-1-yl, 5-hexen-1-yl) optionally substituted by 1 to 3 halogen atoms (e.g. fluorine, chlorine, bromine, iodine) and a lower alkynyl group (e.g. a C2-6 alkynyl group such as 2-butyn-1-yl, 4-pentyn-1-yl, 5-hexyn-1-yl) optionally substituted by 1 to 3 halogen atoms (e.g. fluorine, chlorine, bromine, iodine), etc. are used.
As the xe2x80x9coptionally substituted lower alkoxy groupxe2x80x9d, for example, a lower alkoxy group (e.g. a C1-6 alkoxy group such as methoxy, ethoxy, propoxy, isopropoxy, n-butoxy, isobutoxy, sec-butoxy, tert-butoxy) optionally having 1 to 3 halogen atoms (e.g. fluorine, chlorine, bromine, iodine), mono- or di-lower alkylamino groups (e.g. mono- or di-C1-6 alkylamino such as methylamino, dimethylamino, ethylamino, dimethylamino) or lower alkoxy-carbonyl groups (e.g. a C1-6 alkoxy-carbonyl group such as methoxycarbonyl, ethoxycarbonyl), etc. are used.
As the xe2x80x9coptionally halogenated lower alkylthio groupxe2x80x9d, for example, a lower alkylthio group (e.g. a C1-6 alkylthio group such as methylthio, fluoromethylthio, ethylthio, n-propylthio, isopropylthio, n-butylthio, isobutylthio, sec-butylthio, tert-butylthio) optionally having 1 to 3 halogen atoms (e.g. fluorine, chlorine, bromine, iodine), etc. exemplified, and as specific examples, for example, methylthio, difluoromethylthio, trifluoromethylthio, ethylthio, propylthio, isopropylthio, butylthio, 4,4,4-trifluorobutylthio, pentylthio, hexylthio, etc. are used.
As specific examples of the condensed ring formed by Ar1xe2x80x2, Ar2xe2x80x2 and the adjacent carbon atom, for example, a condensed ring represented by the formula: 
wherein R8 is same as defined above, etc. are used.
As Ar1xe2x80x2 and Ar2, same or different and are independently, a C6-14 aromatic hydrocarbon group optionally having a substituent is preferable and a phenyl group optionally having a substituent is more preferable. More specifically, as Ar1xe2x80x2 and Ar2xe2x80x2, independently, (1) a phenyl group which may be substituted by a halogen atom or C1-6 alkyl, etc. are preferable and particularly an unsubstituted phenyl group is preferable.
In the above mentioned formula, the ring Bxe2x80x2 represents a 6-membered nitrogen-containing heterocycle optionally having a substituent.
As the 6-membered nitrogen-containing heterocycle represented by the ring Bxe2x80x2, for example, a 6-membered nitrogen-containing heterocycle containing at least one nitrogen atom and further optionally containing 1 to 3 hetero atoms selected from, e.g., by a nitrogen atom, an oxygen atom and a sulfur atom, etc. are used. In the above mentioned formula (I), it is preferable that a bivalent group removed one hydrogen atom from the nitrogen atom and others atom of the ring Bxe2x80x2, respectively, is formed. Specifically, a 6 membered nitrogen atom-containing heterocyclic group such as 
etc. are preferable.
As the substituents of the 6-membered nitrogen atom-containing heterocycle represented by the ring Bxe2x80x2, for example, the same substituents of the xe2x80x9caromatic group optionally having a substituentxe2x80x9d represented by Ar1xe2x80x2 and Ar2xe2x80x2 as mentioned above, etc. are used.
As specific preferable examples of the ring Bxe2x80x2, for example, a ring represented by the formula: 
wherein Z is a nitrogen atom or a methine group, Z1xe2x80x3 and Z2xe2x80x3 are independently an ethylene group which may be substituted by a hydroxy group, an oxo group or a C1-6 alkyl group, etc. are used.
As the C1-6 alkyl group which is a substituent for the ethylene group represented by Z1xe2x80x3 and Z2xe2x80x3, for example, a linear or branched C1-3 alkyl group such as methyl, ethyl, propyl, isopropyl, butyl, isobutyl, sec-butyl, tert-butyl, pentyl, hexyl, etc. are used.
Preferable examples of the xe2x80x9cethylene group which may be substituted by a hydroxy group, an oxo group or a C1-6 alkyl groupxe2x80x9d are an unsubstituted methylene group and an unsubstituted ethylene group, and particularly an unsubstituted ethylene group is preferable.
As more preferable examples of the ring Bxe2x80x2, a 6-membered ring represented by the formula: 
particularly 
etc. are preferable.
In the above mentioned formula, X and Y represent the same meanings as mentioned above, and the same preferable groups as mentioned above are used.
In the above mentioned formula, A represents the same meaning as mentioned above, and the same preferable groups as mentioned above are used. Among them, as A, a nitrogen atom or CR7xe2x80x2 wherein R7xe2x80x2 is a hydrogen atom, a halogen atom, a C1-6 alkyl group, a C1-6 alkoxy-carbonyl group or a carboxyl group is preferable and particularly a nitrogen atom or CH is preferable.
R1xe2x80x2 represents a hydrocarbon group substituted by an optionally esterified carboxyl group.
As the hydrocarbon group represented by R1xe2x80x2, for example, the same those as the hydrocarbon group represented by R7 are used. Among them, a C1-6 alkyl group such as methyl, ethyl, propyl, isopropyl, butyl, sec-butyl, tert-butyl, etc. are preferable, and particularly an isopropyl group is preferable.
As the xe2x80x9coptionally esterified carboxyl groupxe2x80x9d which is a substituent for the hydrocarbon group represented by R1xe2x80x2, a group represented by the formula: xe2x80x94COOR11 wherein R11 is a hydrogen atom or a hydrocarbon group which may be substituted, etc. are used.
As the hydrocarbon group which may be substituted represented by R11, for example, the same those as the hydrocarbon group optionally having a substituent represented by R7 are used. Among them, a C1-6 alkyl group such as methyl, ethyl, propyl, isopropyl, butyl, sec-butyl, tert-butyl, etc. are preferable, and particularly an ethyl group is preferable.
As the xe2x80x9coptionally esterified carboxyl groupxe2x80x9d, for example, a carboxyl group optionally esterified with a C1-6 alkyl group, etc. are preferable.
As R1xe2x80x2, for example, a C1-6 alkyl group which may be substituted by carboxyl or C1-6 alkoxy-carbonyl (particularly, ethoxycarbonyl, etc.), etc. are preferable and particularly a carboxyl dimethylmethyl group or an ethoxycarbonyl dimethylmethyl group are preferred.
In the above mentioned formula, R2 and R3 represent the same meanings as mentioned above, and the same preferable groups as mentioned above are used.
In the above mentioned formula, R8 represents the same meaning as mentioned above and the same preferable groups mentioned above are use.
As the subjected compound (Ixe2x80x2) of the method for producing of the present invention, a compound wherein Ar1xe2x80x2 and Ar2xe2x80x2 are, independently a phenyl group which may be substituted by a halogen atom or C1-6 alkyl; the ring Bxe2x80x2 is a ring represented by the formula: 
wherein Z is a nitrogen atom or a methyne group, Z1xe2x80x3 and Z2xe2x80x3 are independently an ethylene group which may be substituted by a hydroxy group, an oxo group or a C1-6 alkyl group;
X is a bond, an oxygen atom or NH;
Y is a group represented by
(i) a C1-6 alkylene group,
(ii) xe2x80x94(CH2)p1Oxe2x80x94,
(iii) xe2x80x94(CH2)p1NHxe2x80x94,
(iv) xe2x80x94(CH2)p1Sxe2x80x94,
(v) xe2x80x94(CH2)q1CH(OH)(CH2)q2Oxe2x80x94,
(vi) xe2x80x94(CH2)q1CH(OH)(CH2)q2NHxe2x80x94,
(vii) xe2x80x94(CH2)q1CH(OH)(CH2)q2Sxe2x80x94,
(viii) xe2x80x94(CH2)p1CONHxe2x80x94,
(ix) xe2x80x94COO(CH2)p1Oxe2x80x94,
(x) xe2x80x94COO(CH2)p1NHxe2x80x94,
(xi) xe2x80x94COO(CH2)p1Sxe2x80x94,
(xii) xe2x80x94(CH2)q1O(CH2)q2Oxe2x80x94,
(xiii) xe2x80x94(CH2)q1O(CH2)q2NHxe2x80x94 or
(xiv) xe2x80x94(CH2)q1O(CH2)q2Sxe2x80x94 wherein p1 is an integer of 1 to 6, q1 and q2 are an integer of 1 to 3, respectively;
A is a nitrogen atom or CR7xe2x80x2 wherein R7xe2x80x2 is a hydrogen atom, a halogen atom, a C1-6 alkyl group, a C1-6 alkoxy-carbonyl group or a carboxyl group;
R1xe2x80x2 is a C1-6 alkyl group which may be substituted by carboxyl, C1-6 alkoxy-carbonyl;
R2 is a hydrogen atom, a C1-6 alkyl group, a C1-6 alkoxy-carbonyl group or a carboxyl group;
R3 is a hydrogen atom;
R8 is a hydrogen atom or a hydroxyl group, is preferable.
Particularly, a compound wherein Ar1xe2x80x2 and Ar2xe2x80x2 are independently a phenyl group; ring Bxe2x80x2 is a group represented by the formula: 
X is a bond or an oxygen atom; Y is a group represented by the formula: xe2x80x94(CH2)p1NHxe2x80x94 wherein p1 is an integer of 1 to 6; A is CR7xe2x80x3 wherein R7xe2x80x3 is a hydrogen atom or a C1-6 alkyl group; R1 is a C1-6 alkyl group which may be substituted by carboxyl or C1-6 alkoxy-carbonyl; R2 is a hydrogen atom; R3 is a hydrogen atom; and R8 is a hydrogen atom, is preferable.
Moreover, a compound wherein Ar1 and Ar2 are independently a phenyl group; ring B is 
X is an oxygen atom; Y is a trimethyleneamino group; R8 is a hydrogen atom; A is CH; R1 is a carboxyl dimethylmethyl group; and R2 and R3 are a hydrogen atom (particularly a hydrate such as dihydrate of the compound), and a compound wherein Ar1 and Ar2 are independently a phenyl group; ring B is 
X is an oxygen atom; Y is a propyl group; R8 is a hydrogen atom; A is CH; R1 is an ethoxycarbonyl dimethylmethyl group;
and R2 and R3 are a hydrogen atom (particularly fumarate such as difumarate of the compound), are preferable.
In the above mentioned formula (Ixe2x80x3), R represents a hydrogen atom or an ethyl group. As R, a hydrogen atom is preferable.
As the hydrate of compound (Ixe2x80x3), for example, a hydrate containing 1 to 5 H2O is used, and of them dihydrate is preferable.
As the succinate of compound (Ixe2x80x3), for example, a salt with 1 to 2 succinic acids is used, and of them a salt with disuccinic acids is preferable.
As the citrate of compound (Ixe2x80x3), for example, a salt with 1 to 2 citric acids is used, and of them a salt with one citric acid is preferable.
The succinate or citrate of the compound (Ixe2x80x3) may be a hydrate or anhydride. As the hydrates of the succinate or citrate of the compound (Ixe2x80x3), for example, a hydrate containing 1 to 5 H2O is used.
As the succinate or citrate of the compound (Ixe2x80x3), an anhydride is preferable.
Preferable example of the compound (Ixe2x80x3) is a hydrate when R is a hydrogen atom, and is a salt with disuccinic acids or a salt with one citric acid when R is an ethyl group.
As the compound of the present invention, particularly,
{circle around (1)} 2-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]imidazo[1,2-b]pyridazin-2-yl]-2-methylpropionic acid dihydrate,
{circle around (2)} Ethyl 2-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]imidazo[1,2-b]pyridazin-2-yl]-2-methylpropionate disuccinate, and
{circle around (3)} Ethyl 2-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]imidazo[1,2-b]pyridazin-2-yl]-2-methylpropionate citrate are preferable.
And,
{circle around (1)} 2-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]-3-methylimidazo[1,2-b]pyridazin-2-yl]-2-methylpropionic acid (compound (Ia)) or a salt thereof,
{circle around (2)} N-[6-[3-[4-(diphenylmethoxy)piperidino]propylamino]-3-methylimidazo[1,2-b]pyridazin-2-carbonyl]glycine (compound (Ib)) or a salt thereof, etc. are preferably used.
Salts of the compound (Ia), or (Ib) include, for example, salts with inorganic acids (e.g., hydrochloric acid, phosphoric acid, hydrobromic acid, sulfuric acid) and salts with organic acids (e.g., acetic acid, formic acid, propionic acid, fumaric acid, maleic acid, succinic acid, tartaric acid, citric acid, malic acid, oxalic acid, methane sulfonic acid, benzene sulfonic acid). Provided that these compounds have an acidic group such as that of a carboxylic acid, as a substituent thereof, the acidic group may form a salt with an inorganic base (e.g., an alkali metal or alkaline earth metal such as sodium, potassium, calcium or magnesium, or ammonia) or an organic base (e.g., a tri-C1-3 alkylamine such as triethylamine).
The compound (Ia), (Ib) or a salt thereof may be an anhydride or a hydrate. Examples of the hydrates of the compound (Ia), (Ib) or a salt thereof are a hydrate containing 1 to 5 H2O, particularly dihydrate.
A pro-drug of the above mentioned compound (I), (Ixe2x80x2), (Ixe2x80x3), (Ia), (Ib) or a salt thereof (hereinafter referred to as the compound of the present invention) means a compound which is converted to the compound of the present invention under the physiological condition or with a reaction due to an enzyme, an gastric acid, etc. in vivo, that is, a compound which is converted to the compound of the present invention with oxidation, reduction, hydrolysis, etc. according to an enzyme; a compound which is converted to the compound of the present invention with gastric acid, etc.
Examples of the pro-drug of the compound of the present invention include a compound wherein an amino group of the compound of the present invention is substituted with acyl, alkyl and phosphoryl group, etc. (e.g. a compound wherein an amino group of the compound of the present invention is substituted with eicosanoyl, alanyl, pentylaminocarbonyl, (5-methyl-2-oxo-1,3-dioxolen-4-yl)methoxycarbonyl, tetrahydrofuranyl, pyrrolidylmethyl, pivaloyloxymethyl, tert-butyl group, etc.); a compound wherein an hydroxy group of the compound of the present invention is substituted with acyl, alkyl, phosphoryl, boryl group, etc. (e.g. a compound wherein an hydroxy group of the compound of the present invention is substituted with acetyl, palmitoyl, propanoyl, pivaloyl, succinyl, fumaryl, alanyl, dimethylaminomethylcarbonyl, etc.); a compound wherein a carboxyl group of the compound of the present invention is modified with ester, amide, etc. (e.g. a compound wherein a carboxyl group of the compound of the present invention is modified with ethyl ester, phenyl ester, carboxymethyl ester, dimethylaminomethyl ester, pivaloyloxymethyl ester, ethoxycarbonyloxyethyl ester, phthalidyl ester, (5-methyl-2-oxo-1,3-dioxolen-4-yl)methyl ester, cyclohexyloxycarbonylethyl ester, methyl amide, etc.); etc. These pro-drug can be produced by per se known method from the compound of the present invention.
The pro-drug of the compound of the present invention may be a compound which is converted into the compound of the present invention under the physiological conditions as described in xe2x80x9cPharmaceutical Research and Developmentxe2x80x9d, Vol. 7 (Drug Design), pages 163-198 published in 1990 by Hirokawa Publishing Co. (Tokyo, Japan).
Methods for producing the compound (I) including the compound. (Ixe2x80x3), (Ia) and (Ib) are mentioned below.
(A) The compound (I) of the present invention or a salt thereof can be produced by reacting a compound represented by the formula: 
wherein Q1 represents a leaving group; the other symbols have the same definitions as those shown above, or a salt thereof, with a compound represented by the formula: 
wherein Q2 represents a leaving group; the other symbols have the same definitions as those shown above, or a salt thereof.
As the leaving group represented by Q1, for example, alkali metals such as sodium and potassium, etc. are used. And, Q1 may be a hydrogen atom.
As the leaving group represented by Q2, a halogen group (e.g., chloro, bromo, iodo), a C6-10 arylsulfonyloxy group (e.g., benzenesulfonyloxy, p-tolylsulfonyloxy), a C1-4 alkyl-sulfonyloxy group (e.g., methanesulfonyloxy), etc. are used.
In this reaction, the compound (IIxe2x80x2) or a salt thereof is normally used at 1 to 5 mol, preferably 1 to 2 mol, per mol of the compound (IIIxe2x80x2) or a salt thereof. This condensation reaction is preferably carried out in the presence of a base. As the base, for example, alkali metal hydrides such as sodium hydride and potassium hydride; alkali metal alkoxides such as sodium methoxide and sodium ethoxide; alkali metal hydroxides such as sodium hydroxide and potassium hydroxide; and alkali metal carbonates such as sodium carbonate and potassium carbonate, etc. are used.
In addition, this reaction can also be carried out in an inert solvent exemplified by alcohols such as methanol and ethanol; ethers such as dioxane and tetrahydrofuran; aromatic hydrocarbons such as benzene, toluene and xylene; nitriles such as acetonitrile; amides such as N,N-dimethylformamide and N,N-dimethylacetamide; and sulfoxides such as dimethyl sulfoxide.
Reaction temperature is normally 10 to 200xc2x0 C., preferably 50 to 100xc2x0 C.
Reaction time is normally 30 minutes to 24 hours, preferably 1 to 6 hours.
(B) Also, the compound (I) of the present invention or a salt thereof can be produced by reacting a compound represented by the formula: 
wherein the symbols have the same definitions as those shown above, or a salt thereof, with a compound represented by the formula: 
wherein the symbols have the same definitions as those shown above, or a salt thereof.
In this reaction, the compound (IV) or a salt thereof is normally used at 1 to 5 mol, preferably 1 to 2 10 mol, per mol of the compound (IIIxe2x80x2) or a salt thereof. This condensation reaction is preferably carried out in the presence of a base. As the base, for example, alkali metal hydrides such as sodium hydride and potassium hydride; alkali metal alkoxides such as sodium methoxide and sodium ethoxide; alkali metal hydroxides such as sodium hydroxide and potassium hydroxide; and alkali, metal, carbonates, such as sodium carbonate and potassium carbonate, etc, are used.
In addition, this reaction can also be carried out in an inert solvent exemplified by alcohols such as methanol and ethanol; ethers such as dioxane and tetrahydrofuran; aromatic hydrocarbons such as benzene, toluene and xylene; nitrites such as acetonitrile; amides such as N,N-dimethylformamide and N,N-dimethylacetamide; and sulfoxides such as dimethyl sulfoxide.
Reaction temperature is normally 10 to 200xc2x0 C., preferably 50 to 100xc2x0 C.
Reaction time is normally 30 minutes to 24 hours, preferably 1 to 6 hours.
(C) Also, compound (I) of the present invention or a salt thereof can be produced by reacting a compound represented by the formula: 
wherein the symbols have the same definitions as those shown above, or a salt thereof, with a compound represented by the formula: 
wherein the symbols have the same definitions as those shown above, or a salt thereof.
In this reaction, the compound (V) or a salt thereof is normally used at 1 to 5 mol, preferably 1 to 2 mol, per mol of the compound (VIxe2x80x2) or a salt thereof. This condensation;reaction is preferably carried out in the presence of a base. As the base, alkali metal hydrides such as sodium hydride and potassium hydride; alkali metal alkoxides such as sodium methoxide and sodium ethoxide; alkali metal hydroxides such as sodium hydroxide and potassium hydroxide; and alkali metal carbonates such as sodium carbonate and potassium carbonate, etc. are used.
In addition, this reaction can also be carried out in an inert solvent exemplified by alcohols such as methanol and ethanol; ethers such as dioxane and tetrahydrofuran; aromatic hydrocarbons such as benzene, toluene and xylene; nitrites such as acetonitrile; amides such as N,N-dimethylformamide and N,N-dimethylacetamide; and sulfoxides such as dimethyl sulfoxide.
Reaction temperature is normally 10 to 200xc2x0 C., preferably 50 to 100xc2x0 C.
Reaction time is normally 30 minutes to 24 hours, preferably 1 to 6 hours.
(D) Also, compound (I) of the present invention or a salt thereof can be produced by reacting a compound represented by the formula: 
wherein the symbols have the same definitions as those shown above, or a salt thereof, with a compound represented by the formula: 
wherein the symbols have the same definitions as those shown above, or a salt thereof.
In this reaction, the compound (VII) or a salt thereof is normally used at 1 to 5 mol, preferably 1 to 2 mol, per mol of the compound (VI) or a salt thereof. This condensation reaction is preferably carried out in the presence of abase. As the base, alkali metal hydrides such as sodium hydride and potassium hydride; alkali metal alkoxides such as sodium methoxide and sodium ethoxide; alkali metal hydroxides such as sodium hydroxide and potassium hydroxide; and alkali metal carbonates such as sodium carbonate and potassium carbonate, etc. are used.
In addition, this reaction can also be carried out in an inert solvent exemplified by alcohols such as methanol and ethanol; ethers such as dioxane and tetrahydrofuran; aromatic hydrocarbons such as benzene, toluene and xylene; nitrites such as acetonitrile; amides such as N,N-dimethylformamide and N,N-dimethylacetamide; and sulfoxides such as dimethyl sulfoxide.
Reaction temperature is normally 10 to 200xc2x0 C., preferably 50 to 100xc2x0 C.
Reaction time is normally 30 minutes to 24 hours, preferably 1 to 6 hours.
(E) Also, compound (I) of the present invention or a salt thereof can be produced by reacting a compound represented by the formula: 
wherein the symbols have the same definitions as those shown above, or a salt thereof, with a compound represented by the formula: 
wherein the symbols have the same definitions as those shown above, or a salt thereof.
In this reaction, the compound (VII) or a salt thereof is normally used at 1 to 5 mol, preferably 1 to 2 mol, per mol of the compound (VIII) or a salt thereof.
In addition, this reaction can also be carried out in an inert solvent exemplified by alcohols such as methanol and ethanol; ethers such as dioxane and tetrahydrofuran; aromatic hydrocarbons such as benzene, toluene and xylene; nitrites such as acetonitrile; amides such as N,N-dimethylformamide and N,N-dimethylacetamide; and sulfoxides such as dimethyl sulfoxide.
Reaction temperature is normally 10 to 200xc2x0 C., preferably 5.0 to 100xc2x0 C.
Reaction time is normally 30 minutes to 24 hours, preferably 1 to 6 hours.
When the compound (I) is obtained in free form, it can be converted into a salt by a conventional method. When the compound (I) is obtained as a salt, it can be converted into a free form or another salt by a conventional method. When the compound (I) is obtained as an anhydride, it can be converted into a hydrate by contacting it with a water.
The hydrate of the compound (Ixe2x80x3) and succinate or citrate of the compound (Ixe2x80x3) of the present invention included in the compound (I) are obtained by
(1) reacting a compound represented by the formula: 
wherein Q2 is a leaving group, or a salt thereof with a compound represented by the formula: 
wherein Q2 is a leaving group, R is same as defined in above, or a salt thereof, then adding a water, or
(2) reacting a free form of the compound (Ixe2x80x3) with a succinic acid or citric acid. The conditions of the reaction are same those with the method for producing for the above mentioned compound (I).
The compound of the invention or a salt thereof thus obtained can be isolated and purified by known means such as solvent extraction, pH adjustment, liquid-liquid transformation, salting out, crystallization, recrystallization and chromatography. When the compound of the invention or a salt thereof contains optical isomers, they can be resolved into the R- and S-configurations by an ordinary means of optical resolution.
Salts of the compound (I), (Ia) or (Ib) includes, for example, salts with inorganic acids (e.g., hydrochloric acid, phosphoric acid, hydrobromic acid, sulfuric acid) and salts with organic acids (e.g., acetic acid, formic acid, propionic acid, fumaric acid, maleic acid, succinic acid, tartaric acid, citric acid, malic acid, oxalic acid, methanesulfonic acid, benzenesulfonic acid). Provided that the compound (I), (Ia) or (Ib) has an acidic group such as that of a carboxylic acid, as a substituent thereof, the acidic group may form a salt with an inorganic base (e.g., an alkali metal or alkaline earth metal such as sodium, potassium, calcium or magnesium, or ammonia) or an organic base (e.g., a tri-C1-3 alkylamine such as triethylamine).
Hereinafter described are methods of producing staring compounds (IIxe2x80x2), (IIxe2x80x3), (IIIxe2x80x2), (IIIxe2x80x3), (VIxe2x80x2), (IV) to (VIII) or salts thereof which are used to produce the compound (I) or a salt thereof. Salts of these starting compounds are same those as salts of the compound (I).
The starting compounds (IIxe2x80x2), (IIxe2x80x3) and (IV) or salts thereof can, for example, be synthesized by the method described in the Journal of Medicinal Chemistry, Vol. 32, p. 583 (1989), or a modification thereof.
The starting compounds (IIIxe2x80x2), (IIIxe2x80x3) or salts thereof can, for example, be synthesized by the method described in the Journal of Organic Chemistry, Vol. 39, p. 2143 (1974) or a modification thereof.
The starting compound (V) or a salt thereof can, for example, be synthesized by the methods described in Japanese Patent Unexamined Publication No. 2739/1987 etc., or modifications thereof.
The starting compounds (VI) and (VIII) or salts thereof can, for example, be synthesized by the methods described in Japanese Patent Unexamined Publication No. 223287/1991, or modifications thereof.
The starting compound (VII) or a salt thereof can, for example, be synthesized by the method described in the Journal of Medicinal Chemistry, Vol. 38, p. 2472 (1995), or a modification thereof.
Although these starting compounds or salts thereof thus obtained can be isolated and purified by known means such as solvent extraction, pH adjustment, liquid-liquid transformation, salting-out, crystallization, recrystallization and chromatography, they may be used as starting materials for the next process, in the form of reaction mixture without purification.
Also, when the starting compound used in each of the reactions for synthesizing the above-described desired compounds and starting compounds has an amino group, a carboxyl group or a hydroxyl group as a substituent, these substituents may have a protective group in common use in peptide chemistry etc.; the desired compound can be obtained by removing, as appropriate, the protective group after completion of the reaction.
The amino group-protecting groups include, for example, formyl, C1-6 alkylcarbonyls that may have a substituent (e.g., acetyl, ethylcarbonyl), phenylcarbonyl, C1-6 alkyl-oxycarbonyls (e.g., methoxycarbonyl, ethoxycarbonyl), phenyloxycarbonyl, C7-10 aralkyl-carbonyls (e.g., benzylcarbonyl), trityl, phthaloyl and N,N-dimethylaminomethylene. Substituents for these groups include halogen atoms (e.g., fluoro, chloro, bromine, iodine), C1-6 alkyl-carbonyls (e.g., methylcarbonyl, ethylcarbonyl, butylcarbonyl) and nitro groups, the number of substituents being about 1 to 3.
The carboxyl group-protecting groups include, for example, C1-6 alkyls that may have a substituent (e.g., methyl, ethyl, n-propyl, isopropyl, n-butyl, tert-butyl), phenyl, trityl and silyl. Substituents for these groups include halogen atoms (e.g., fluoro-, chloro, bromine, iodine), formyl, C1-6 alkyl-carbonyls (e.g., acetyl, ethylcarbonyl, butylcarbonyl) and nitro groups, the number of substituents being about 1 to 3.
The hydroxyl group-protecting groups include, for example, C1-6 alkyls that may have a substituent (e.g. methyl, ethyl, n-propyl, isopropyl, n-butyl, tert-butyl), phenyl, C7-10 aralkyls (e.g., benzyl), formyl, C1-6 alkyl-carbonyls (e.g., acetyl, ethylcarbonyl), phenyloxycarbonyl, benzoyl, C7-10 aralkyl-carbonyls (e.g., benzylcarbonyl), pyranyl, furanyl and silyl. Substituents for these groups include halogen atoms. (e.g., fluoro, chloro, bromine, iodine), C1-6 alkyls (e.g., methyl, ethyl, n-propyl), phenyl, C7-10 aralkyls (e.g., benzyl) and nitro groups, the number of substituents being about 1 to 4.
The protecting groups can be removed by commonly known methods or modifications thereof, including treatments with acids, bases, reducing agents, ultraviolet rays, hydrazine, phenylhydrazine, sodium N-methyldithiocarbamate, tetrabutylammonium fluoride, palladium acetate etc.
According to the method of the present invention, the compound (Ixe2x80x2) or a salt thereof can be produced by reacting a compound represented by the formula: 
wherein Q1 represents a leaving group; the other symbols have the same definitions as those shown above, or a salt thereof, with a compound represented by the formula: 
wherein Q2 represents a leaving group; the other symbols have the same definitions as those shown above, or a salt thereof, in a solvent or/and in the presence of a base.
As the leaving group represented by Q1, alkali metals such as lithium, sodium and potassium, etc. are used. And, Q1 may be a hydrogen atom.
As the leaving group represented by Q2, a halogen atom (e.g., chloro, bromine, iodine), a C6-10 arylsulfonyloxy group (e.g., benzenesulfonyloxy, p-tolylsulfonyloxy), a C1-4 alkyl-sulfonyloxy group (e.g., methanesulfonyloxy), etc. are used.
As the solvent used in the method of the present invention, for example, a non-proton solvent having a high boiling point, etc. are used. The boiling point of the solvent are, for example, about 90 to about 220xc2x0 C., preferably about 110 to about 160xc2x0 C.
As the solvent,
(1) ethers such as dioxane and tetrahydrofuran,
(2) aromatic hydrocarbons such as benzene, toluene and xylene,
(3) nitriles such as acetonitrile,
(4) straight chained or cyclic amides such as N,N-dimethylformamide, N,N-dimethylacetamide and 1-methyl-2-pyrrolidone,
(5) sulfoxides such as dimethyl sulfoxide,
(6) cyclic sulfones such as sulfolane,
(7) halogenated hydrocarbons such as dichloroethane and chloroform,
(8) azoles such as imidazole, 2-methylimidazole and pyridine, etc. are used. Of them, cyclic amides such as 1-methyl-2-pyrrolidone, sulfoxides such as dimethyl sulfoxide, cyclic sulfones such as sulfolane, etc. are preferred, and cyclic amides such as 1-methyl-2-pyrrolidone, sulfoxides such as dimethylsulfoxide, etc. are more preferred, and particularly sulfoxides such as dimethyl sulfoxide, etc. are preferred. And, alcohols such as methanol, ethanol, etc. may be used as the solvent.
As the base used in the method of the present invention, for example,
(1) alkali metal hydrides such as sodium hydride and potassium hydride,
(2) alkali metal alkoxides such as sodium methoxide, sodium ethoxide and sodium t-butoxide,
(3) alkali metal hydroxides such as sodium hydroxide and potassium hydroxide,
(4) alkali metal carbonates such as lithium carbonate, sodium carbonate and potassium carbonate, etc. are used. Of them, alkali metal carbonates such as sodium carbonate and potassium carbonate, etc. are preferred, particularly sodium carbonate is more preferred.
The reaction of the present invention is preferably conducted in the solvent and in the presence of the base.
And, additives for promoting the reaction can be used in the method of the present invention. Examples of the additives are magnesium sulfate, zinc chloride, cuprous chloride (CuCl), potassium fluoride, lithium chloride and so on.
In this reaction, the compound (II) or a salt thereof is normally used at about 1 to about 5 mol, preferably about 1 to about 2 mol, per mol of the compound (III) or a salt thereof.
And, a volume of the compound (II) or a salt thereof can be reduced by conducting the reaction of the present invention in the presence of a base, particularly alkali metal carbonate such as sodium carbonate, comparing the reaction in the presence of no base. When the reaction is conducted in the presence of a base, the compound (II) or a salt thereof is normally used at about 1.0 to about 1.7 mol, preferably about 1.5 mol, per mol of the compound (III) or a salt thereof.
Reaction temperature is normally about 10 to 200xc2x0 C., preferably about 100 to about 180xc2x0 C., more preferably about 110 to 160xc2x0 C.
Reaction time is normally about 30 minutes to about 30 hours, preferably about 30 minutes to about 24 hours, more preferably about 1 hour to about 6 hours.
And, the reaction of the present invention can be conducted in an atmosphere of inert gas such as N2 gas, argon gas, etc.
Particularly, when the compound (Ixe2x80x2) wherein Ar1xe2x80x2 and Ar2xe2x80x2 are independently a phenyl group; ring Bxe2x80x2 is 
X is an oxygen atom; Y is a propylamino group; R8 is a hydrogen atom; A is CH; R1xe2x80x2 is a carboxyl dimethylmethyl group; and R2 and R3 are a hydrogen atom, or a salt thereof is produced, as the solvent, a dimethylsulfoxide, etc. are preferable and as the base, a sodium carbonate, etc. are preferable.
And, when the compound (Ixe2x80x2) wherein Ar1xe2x80x2 and Ar2xe2x80x2 are independently a phenyl group; ring Bxe2x80x2 is 
X is an oxygen atom; Y is a propylamino group; R8 is a hydrogen atom; A is CH; R1xe2x80x2 is an ethoxycarbonyl dimethylmethyl group; and R2 and R3 are a hydrogen atom, or a salt thereof is produced, as the solvent, a 1-methyl-2-pyrolidone, dimethylsulfoxide, etc. are preferable and as the base, a sodium carbonate, etc. are preferable.
Furthermore, this reaction can be conducted in the presence of halogenated alkali metals. As the halogenated alkali metals, a sodium chloride, a sodium fluoride, a sodium bromide, etc. are used, and particularly a sodium bromide is preferable. Thus by adding the halogenated alkali metals, amounts of the subjected compound can increase.
Particularly, when the compound (Ixe2x80x2) wherein Ar1xe2x80x2 and Ar2xe2x80x2 are independently a phenyl group; ring Bxe2x80x2 is 
X is an oxygen atom; Y is a propylamino group; R8 is a hydrogen atom; A is CH; R1xe2x80x2 is a carboxyl dimethylmethyl group; and R2 and R3 are a hydrogen atom, or a salt thereof is produced, as the solvent, a dimethylsulfoxide, etc. are preferable and as the base, a sodium carbonate, etc. are used and as the halogenated alkali metals, a sodium bromide, etc. are used.
When the halogenated alkali metals are used, the halogenated alkali metals are normally used at about 0.05 to about 0.25 mol, preferably about 0.1 to about 0.15 mol, per mol of the compound (II) or a salt thereof.
When the compound (Ixe2x80x2) is obtained in free form, it can be converted into a salt by a conventional method. When the compound (Ixe2x80x2) is obtained as a salt, it can be converted into a free form or another salt by a conventional method. The compound (I) or a salt thereof thus obtained can be isolated and purified by known means such as solvent extraction, pH adjustment, liquid-liquid transformation, salting out, crystallization, recrystallization and chromatography. When the compound (Ixe2x80x2) or a salt thereof contains optical isomers, it can be resoluted into the R- and S-configurations by an ordinary means of optical resolution.
Hereinafter described are methods of producing staring compounds (II) and (III) or salts thereof which are used to produce the compound (Ixe2x80x2) or a salt thereof.
Salts of the compounds (Ixe2x80x2), (II) and (III) include, for example, salts with inorganic acids (e.g., hydrochloric acid, phosphoric acid, hydrobromic acid, sulfuric acid) and salts with organic acids (e.g., acetic acid, formic acid, propionic acid, fumaric acid, maleic acid, succinic acid, tartaric acid, citric acid, malic acid, oxalic acid, methanesulfonic acid, benzenesulfonic acid). Provided that these compounds have an acidic group such as that of a carboxylic acid, as a substituent thereof, the acidic group may form a salt with an inorganic base (e.g., an alkali metal or alkaline earth metal such as sodium, potassium, calcium or magnesium, or ammonia) or an organic base (e.g., a tri-C1-3 alkylamine such as triethylamine).
When the compound (Ixe2x80x2) has an ester group in the molecule, it can be converted to a carboxylic acid thereof by a conventional hydrolysis. And, When the compound (Ixe2x80x2) has a carboxylic acid group in the molecule, it can be converted to an esther thereof by a conventional estherification.
The starting compounds (II) or salts thereof can, for example, be synthesized by the method described in the Journal of Medicinal Chemistry, Vol. 32, p. 583 (1989), or a modification thereof.
The starting compound (III) or a salt thereof can, for example, be synthesized by the method described in the Journal of Organic Chemistry, Vol. 39, p. 2143 (1974) or a modification thereof.
Although these starting compounds or salts thereof thus obtained can be isolated and purified by known means such as solvent extraction, pH ajustment, liquid-liquid transformation, salting-out, crystallization, recrystallization and chromatography, they may be used as starting materials for the next process, in the form of reaction mixture without purification.
Also, when the starting compound used in each of the reactions for synthesizing the above-described desired compounds and starting compounds has an amino group, a carboxyl group or a hydroxyl group as a substituent, these substituents may have a protective group in common use in peptide chemistry etc.; the desired compound can be obtained by removing, as appropriate, the protective group after completion of the reaction.
Examples of the amino group-protecting groups, the carboxyl group-protecting groups, the hydroxyl group-protecting groups are same those mentioned above.
The protecting groups can be removed by commonly known methods or modifications thereof, including treatments with acids, bases, reducing agents, ultraviolet rays, hydrazine, phenylhydrazine, sodium N-methyldithiocarbamate, tetrabutylammonium fluoride, palladium acetate, etc.
The compound (I) of the present invention, a salt thereof or a pro-drug thereof can be safely used as an anti-allergic agent in mammals (e.g., human, mice, dogs, rats, bovines), because it exhibits excellent anti-allergic, anti-histaminic, anti-inflammatory, anti-PAF (platelet activating factor) or eosinophil chemotaxis inhibiting activity, etc., with low toxicity (acute toxicity: LD50 greater than 2 g/kg). The,compound (I), a salt thereof or a pro-drug thereof exhibits an eosinophil chemotaxis inhibiting activity as well as an anti-histaminic activity, and can be used to prevent or treat allergic skin diseases such as eczematous dermatitis, contact dermatitis, pruritus, dried dermatitis, acute urticaria, prurigo, etc., and inflammatory dermatosis such as atopic dermatitis, etc.
The hydrate of the compound (Ixe2x80x3) has an excellent stability exceeding that of an anhydride of the compound (Ixe2x80x3).
The succinate or citrate of the compound (Ixe2x80x3) has an excellent stability exceeding that of a fumarate of the compound (Ixe2x80x3).
The compound (Ixe2x80x2) or a salt thereof, the hydrate of the compound (Ixe2x80x3), the succinate or citrate of the compound (Ixe2x80x3), compound (Ia), (Ib) or a salt thereof, or a pro-drug thereof can be safely used as an anti-allergic agent in mammals (e.g., human, mice, dogs, rats, bovines), because it exhibits excellent anti-allergic, anti-histaminic, anti-inflammatory, anti-PAF (platelet activating factor) or eosinophil chemotaxis inhibiting activity, etc., with low toxicity (acute toxicity: LD50 greater than 2 g/kg). The compound (Ixe2x80x2) or a salt thereof, the hydrate of the compound (Ixe2x80x3), the succinate or citrate of the compound (Ixe2x80x3), compound (Ia), (Ib) or a salt thereof, or a pro-drug thereof exhibits an eosinophil chemotaxis inhibiting activity as well as an anti-histaminic activity, and can be used to prevent or treat allergic diseases such as chronic urticaria, atopic dermatitis, allergic rhinitis, allergic conjunctivitis and hypersensitive pneumonitis; dermal diseases (particularly, allergic skin diseases) such as eczema, herpetic dermatitis and psoriasis; and respiratory diseases such as eosinophilic pneumonia (PIE syndrome), chronic obstructive pulmonary disease (COPD) and asthma, etc., in the above-mentioned mammals. Preferably, these compounds can be used to prevent or treat asthma, allergic conjunctivitis, allergic rhinitis, chronic urticaria and atopic dermatitis.
Furthermore, the compound (I) or a salt thereof, the compound (Ixe2x80x2) or a salt thereof, the hydrate of the compound (Ixe2x80x3), the succinate or citrate of the compound (Ixe2x80x3), preventing increase of intranasal pressure, sneezing frequency, nasal secretion, pollinosis, hypersensitivity of upper respiratory tract, etc.
Route of administration may be oral or another route.
Also, the preparation for the present invention may contain as active ingredients pharmaceutical components other than the compound (I) or a salt thereof, the compound (Ixe2x80x2) or a salt thereof, the hydrate of the compound (Ixe2x80x3), the succinate or citrate of the compound (Ixe2x80x3), or a pro-drug thereof (thereinafter referred to as the compound of the resent invention).
Such pharmaceutically active components include, for example, anti-asthmatics (e.g., theophylline, procaterol, ketotifen, azelastine, seratrodast), anti-allergic agents (e.g., ketotifen, terfenadine, azelastine, epinastine), anti-inflammatory agents (e.g., diclofenac sodium, ibuprofen, indomethacin), antibacterial agents (e.g., cefixime, cefdinir, ofloxacin, tosufloxacin) and antifungal agents (e.g., fluconazole, itraconazole). These components are not subject to limitation, as long as the object of the present invention is accomplished, and may be used in appropriate mixing ratios. Useful dosage forms include, for example, tablets (including sugar-coated tablets and film-coated tablets), pills, capsules (including microcapsules), granules, fine granules, powders, syrups, emulsions, suspensions, injectable preparations, inhalants and ointments. These preparations are prepared by conventional methods (e.g., methods described in the Pharmacopoeia of Japan).
In the preparation of the present invention, the content of the compound (I) or a salt thereof is normally about 0.01 to about 100% by weight, preferably about 0.1 to about 50% by weight, and more preferably about 0.5 to about 20% by weight, relative to the entire preparation, depending on the form of the preparation.
Specifically, tablets can be produced by granulating a pharmaceutical as-is, or in a uniform mixture with excipients, binders, disintegrating agents and other appropriate additives, by an appropriate method, then adding lubricants etc., and subjecting the mixture to compressive shaping, or by subjecting to direct compressive shaping a pharmaceutical as-is, or in a uniform mixture with excipients, binders, disintegrating agents and other appropriate additives, or subjecting to compressive shaping previously prepared granules as-is, or in a uniform mixture with appropriate additives. These tablets may incorporate coloring agents, correctives etc. as necessary, and may be coated with appropriate coating agents.
Injectable preparations can be produced by dissolving, suspending or emulsifying a given amount of a pharmaceutical in an aqueous solvent such as water for injection, physiological saline or Ringer""s solution, or a non-aqueous solvent such as a vegetable oil, and diluting to a given amount, or transferring a given amount of a pharmaceutical into a container for injection and sealing the container.
Examples of the carriers for oral preparations are substances in common use in pharmaceutical production, such as starch, mannitol, crystalline cellulose and carboxymethyl cellulose sodium. Examples of the carriers for injectable preparations are distilled water, physiological saline, glucose solutions and transfusions. Other additives in common use for pharmaceutical production can also be added,as appropriate.
Depending on patient age, body weight, symptoms, route and frequency of administration and other factors, the daily dose of these preparations is normally about 0.1 to about 100 mg/kg, preferably about 1 to about 50 mg/kg, and more preferably about 1 to about 10 mg/kg, based on daily dose of active ingredient (the compound (I) or a salt thereof), once or in two portions daily for each asthmatic adult.